HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS

Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegativ...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Nagoya mathematical journal Jg. 242; S. 1 - 34
Hauptverfasser: MIZUTA, YOSHIHIRO, OHNO, TAKAO, SHIMOMURA, TETSU
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Nagoya Cambridge University Press 01.06.2021
Schlagworte:
Euclidean space
Mathematical functions
ISSN:0027-7630, 2152-6842
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegative, bounded and Hölder continuous of order $\unicode[STIX]{x1D703}\in (0,1]$ and $1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$ . We also establish Sobolev type inequality for Riesz potentials on the unit ball.
AbstractList Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent \(p_{1}(\cdot )\) approaching \(1\) and for double phase functionals \(\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}\), where \(a(x)^{1/p_{2}}\) is nonnegative, bounded and Hölder continuous of order \(\unicode[STIX]{x1D703}\in (0,1]\) and \(1/p_{2}=1-\unicode[STIX]{x1D703}/N>0\). We also establish Sobolev type inequality for Riesz potentials on the unit ball.
Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegative, bounded and Hölder continuous of order $\unicode[STIX]{x1D703}\in (0,1]$ and $1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$ . We also establish Sobolev type inequality for Riesz potentials on the unit ball.
Author SHIMOMURA, TETSU
MIZUTA, YOSHIHIRO
OHNO, TAKAO
Author_xml – sequence: 1
  givenname: YOSHIHIRO
  surname: MIZUTA
  fullname: MIZUTA, YOSHIHIRO
– sequence: 2
  givenname: TAKAO
  orcidid: 0000-0001-6049-811X
  surname: OHNO
  fullname: OHNO, TAKAO
– sequence: 3
  givenname: TETSU
  surname: SHIMOMURA
  fullname: SHIMOMURA, TETSU
BookMark eNptkLtugzAYha0qlZqknfoCljpWpLYxYEaHOAGJAuLS24IMMVKiBFIgQ7e-Q9-wT1KidKo6_cP5zvmlbwJGdVMrAG4xmmGErYd6v50RhO0ZZhdgTLBBNJNRMgJjhIilWaaOrsCk67YIIabb-hgoV8Rv359fj2Eci1eYRNwRCQwDmLoCZoGXwjn3ffjspS584rHH576A4iUKAxGkkEdRHHLH9YIV5MECLsLslEcuTwRcZoGTemHA_eQaXFZy16mb3zsF2VKkjqv54cpzuK-V2DJ7zSyRLS2kaFFQWzFmKmMtC0qKskRSUYJthXWLmcSi0rCqtdJJZZCi0tdyrVhB9Sm4O-8e2ub9qLo-3zbHth5e5sTANqaEMn2g8Jkq26brWlXl5aaX_aap-1ZudjlG-clmPtjMTzZzzIbO_Z_Ood3sZfvxL_0DNuRw4Q
CitedBy_id crossref_primary_10_1007_s13163_019_00332_z
crossref_primary_10_1002_mma_7425
crossref_primary_10_1007_s00025_023_01858_x
Cites_doi 10.1007/s00205-014-0785-2
10.1080/17476930903394697
10.1016/j.jde.2003.11.007
10.21136/CMJ.1991.102493
10.1016/j.na.2017.09.010
10.1016/j.jmaa.2012.03.041
10.1007/s10231-015-0542-7
10.1007/s11118-010-9205-x
10.1002/mana.200410465
10.1016/j.jmaa.2012.04.043
10.4064/sm163-2-4
10.1007/s00205-003-0301-6
10.1007/s13348-017-0210-x
10.32917/hmj/1147883393
10.5186/aasfm.2014.3913
10.1002/mana.200510609
10.1007/s11117-016-0463-8
10.1016/j.jfa.2015.10.002
10.1090/spmj/1392
10.1080/17476933.2014.908857
10.1007/s00009-013-0285-x
10.1007/978-3-642-18363-8
10.1007/s11512-010-0134-0
ContentType Journal Article
Copyright 2019 Foundation Nagoya Mathematical Journal
Copyright_xml – notice: 2019 Foundation Nagoya Mathematical Journal
DBID AAYXX
CITATION
8FE
8FG
ABJCF
AFKRA
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PTHSS
DOI 10.1017/nmj.2019.18
DatabaseName CrossRef
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Materials Science & Engineering
ProQuest Central UK/Ireland
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
Engineering Collection
DatabaseTitle CrossRef
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest One Academic
ProQuest Central (New)
Engineering Collection
ProQuest One Academic (New)
DatabaseTitleList Engineering Database
CrossRef
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2152-6842
EndPage 34
ExternalDocumentID 10_1017_nmj_2019_18
GroupedDBID --Z
-~X
09C
09E
0R~
123
29M
2WC
6OB
7.U
8FE
8FG
AAAZR
AABES
AABWE
AACJH
AAGFV
AAKTX
AANRG
AARAB
AASVR
AAUKB
AAXMD
AAYXX
ABBZL
ABDNZ
ABGDZ
ABJCF
ABJNI
ABLJU
ABMWE
ABQTM
ABROB
ABUFD
ABVKB
ABVZP
ABXAU
ABXHF
ABZCX
ACBMC
ACDLN
ACGFS
ACIPV
ACIWK
ACNCT
ACUIJ
ACYZP
ACZBM
ACZWT
ADCGK
ADDNB
ADFEC
ADKIL
ADOVH
ADOVT
ADVJH
ADYHW
AEBAK
AEHGV
AENCP
AENEX
AENGE
AFFHD
AFFOW
AFFUJ
AFKQG
AFKRA
AFLVW
AFZFC
AGABE
AGBYD
AGJUD
AHQXX
AHRGI
AIGNW
AIHIV
AIOIP
AJAHB
AJCYY
AJPFC
AJQAS
AKMAY
AKZCZ
ALMA_UNASSIGNED_HOLDINGS
ALWZO
AMVHM
AQJOH
ARZZG
ATUCA
AUXHV
AYIQA
BBLKV
BCGOX
BENPR
BESQT
BGLVJ
BJBOZ
BLZWO
BMAJL
CBIIA
CCPQU
CCQAD
CCUQV
CFAFE
CFBFF
CGQII
CHEAL
CITATION
CJCSC
DOHLZ
E3Z
EBS
EGQIC
EJD
HCIFZ
H~9
IH6
IOEEP
IOO
JHPGK
JQKCU
KAFGG
KCGVB
KFECR
L6V
L7B
LHUNA
LW7
M7S
NHB
NIKVX
NZEOI
OHT
OK1
OVT
P2P
PHGZM
PHGZT
PQGLB
PTHSS
PUASD
PYCCK
RAMDC
RBU
RBV
RCA
RDU
ROL
RPE
S6U
SAAAG
T9M
TKC
TN5
TR2
UT1
WFFJZ
WS9
XOL
XSB
YNT
YQT
ZDLDU
ZJOSE
ZMEZD
ZY4
ZYDXJ
DWQXO
PKEHL
PQEST
PQQKQ
PQUKI
ID FETCH-LOGICAL-c176t-6c09a70e4bb49e886e5dab42bcc0ae4219e13786274a57fde32f52bf3dade8b43
IEDL.DBID M7S
ISSN 0027-7630
IngestDate Fri Jul 25 12:05:59 EDT 2025
Sat Nov 29 05:41:07 EST 2025
Tue Nov 18 20:58:04 EST 2025
IsPeerReviewed true
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c176t-6c09a70e4bb49e886e5dab42bcc0ae4219e13786274a57fde32f52bf3dade8b43
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-6049-811X
PQID 2519142483
PQPubID 2046271
PageCount 34
ParticipantIDs proquest_journals_2519142483
crossref_citationtrail_10_1017_nmj_2019_18
crossref_primary_10_1017_nmj_2019_18
PublicationCentury 2000
PublicationDate 2021-06-00
20210601
PublicationDateYYYYMMDD 2021-06-01
PublicationDate_xml – month: 06
  year: 2021
  text: 2021-06-00
PublicationDecade 2020
PublicationPlace Nagoya
PublicationPlace_xml – name: Nagoya
PublicationTitle Nagoya mathematical journal
PublicationYear 2021
Publisher Cambridge University Press
Publisher_xml – name: Cambridge University Press
References S0027763019000187_r13
S0027763019000187_r12
S0027763019000187_r15
S0027763019000187_r14
S0027763019000187_r17
S0027763019000187_r16
S0027763019000187_r19
S0027763019000187_r18
Cruz-Uribe (S0027763019000187_r8) 2003; 28
Mizuta (S0027763019000187_r25) 2000; 20
S0027763019000187_r11
S0027763019000187_r10
S0027763019000187_r3
S0027763019000187_r23
S0027763019000187_r4
S0027763019000187_r5
S0027763019000187_r26
S0027763019000187_r6
S0027763019000187_r1
S0027763019000187_r2
S0027763019000187_r7
Mizuta (S0027763019000187_r24) 2009
S0027763019000187_r9
S0027763019000187_r20
S0027763019000187_r22
Stein (S0027763019000187_r27) 1970
S0027763019000187_r21
References_xml – ident: S0027763019000187_r9
  doi: 10.1007/s00205-014-0785-2
– ident: S0027763019000187_r4
  doi: 10.1080/17476930903394697
– ident: S0027763019000187_r11
  doi: 10.1016/j.jde.2003.11.007
– ident: S0027763019000187_r19
  doi: 10.21136/CMJ.1991.102493
– ident: S0027763019000187_r16
  doi: 10.1016/j.na.2017.09.010
– ident: S0027763019000187_r14
  doi: 10.1016/j.jmaa.2012.03.041
– ident: S0027763019000187_r7
  doi: 10.1007/s10231-015-0542-7
– ident: S0027763019000187_r5
  doi: 10.1007/s11118-010-9205-x
– ident: S0027763019000187_r17
  doi: 10.1002/mana.200410465
– ident: S0027763019000187_r2
  doi: 10.1016/j.jmaa.2012.04.043
– volume-title: Singular Integrals and Differentiability Properties of Functions
  year: 1970
  ident: S0027763019000187_r27
– ident: S0027763019000187_r6
  doi: 10.4064/sm163-2-4
– ident: S0027763019000187_r12
  doi: 10.1007/s00205-003-0301-6
– volume: 20
  start-page: 201
  year: 2000
  ident: S0027763019000187_r25
  article-title: Differentiability and Hölder continuity of Riesz potentials of Orlicz functions
  publication-title: Analysis (Munich)
– ident: S0027763019000187_r20
  doi: 10.1007/s13348-017-0210-x
– ident: S0027763019000187_r13
  doi: 10.32917/hmj/1147883393
– ident: S0027763019000187_r21
  doi: 10.5186/aasfm.2014.3913
– volume: 28
  start-page: 223
  year: 2003
  ident: S0027763019000187_r8
  article-title: The maximal function on variable L p spaces
  publication-title: Ann. Acad. Sci. Fenn. Ser. Math.
– ident: S0027763019000187_r23
  doi: 10.1002/mana.200510609
– ident: S0027763019000187_r15
  doi: 10.1007/s11117-016-0463-8
– ident: S0027763019000187_r18
  doi: 10.1016/j.jfa.2015.10.002
– ident: S0027763019000187_r3
  doi: 10.1090/spmj/1392
– start-page: 193
  volume-title: Potential Theory and Stochastics in Albac
  year: 2009
  ident: S0027763019000187_r24
– ident: S0027763019000187_r22
  doi: 10.1080/17476933.2014.908857
– ident: S0027763019000187_r26
  doi: 10.1007/s00009-013-0285-x
– ident: S0027763019000187_r10
  doi: 10.1007/978-3-642-18363-8
– ident: S0027763019000187_r1
  doi: 10.1007/s11512-010-0134-0
SSID ssj0008393
Score 2.2374563
Snippet Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$...
Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent \(p_{1}(\cdot )\)...
SourceID proquest
crossref
SourceType Aggregation Database
Enrichment Source
Index Database
StartPage 1
SubjectTerms Euclidean space
Mathematical functions
Title HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS
URI https://www.proquest.com/docview/2519142483
Volume 242
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 2152-6842
  dateEnd: 20241207
  omitProxy: false
  ssIdentifier: ssj0008393
  issn: 0027-7630
  databaseCode: M7S
  dateStart: 20160301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2152-6842
  dateEnd: 20241207
  omitProxy: false
  ssIdentifier: ssj0008393
  issn: 0027-7630
  databaseCode: BENPR
  dateStart: 20160301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwELZa4NAeoA-q8ijygUOLlJKHEyenyrt4FaQliZJs2SKkKH5EagvLY7ec-Q_8Q34JmSS7LVLFhXPmEHnsbzzjme9DaNfxlAcsm4arSZ2gWGVQ46CwjVIRV5KKBmbVeHpIo8gfj4OkK7hNu7bKOSY2QK0uJNTI92HCEqayfOfb5ZUBqlHwutpJaLxEy8CSYDete9kCievg374w29Soz5HZzecBZfTk_Bf0dQVfQe3j34j0GJCbKDNYe-7_vUGr3f0Ss3ZDvEUv9OQden20IGedvke_Q56e3N_eHcVpyn_gLGF9nuE4wnnIcZ0P5rjHhkN8fJiH-DtLD1lvyDEfJ3HEoxyzJElj1ocqFz79bJ1-wSw6wAfxCKySkGUcD0ZRv-XYzdbRaMDzfmh0mguGtKg3MzxpBiU1NRGCBNr3Pe2qUhBbSGmWmtT4pi2H-qDYU7q0UtqxK9cWlaNKpX1BnA9oaXIx0R8RVqrObWxTur5QRHpOSSoNS6Q8S7mC0A20N1_3QnaE5KCLcVa0nWe0qJ1UgJMKy99Auwvjy5aH4_9m23PvFN1hnBZ_XbP59Oct9MqGlpWmyLKNlmbXf_QntCJvZj-n1ztoucejJN1p9tgDXOXRNQ
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwELZKQaIc-K8oFPChSIAUmjhOnBwQcnezyqrZJEqysKBKafwTCVq2pbuAuPEOvAcPxZNg52cBCXHrgXNGkZL5_I3HnpkPgB3bFa6esmk4EqsExap8xYMMGZXADsc18c268XRE4tibzfx0DXzve2F0WWXPiQ1RixOuz8h3dYel7sry7BenHwytGqVvV3sJjRYW-_LLZ5WyLZ6Ph8q_jxAaBcUgNDpVAYNbxF0aLjf9ipgSM4Z96XmudETFMGKcm5XEagVLyyae1qSpHFILaaPaQay2RSWkx7Ct3nsBXMSa_ZtSwXzF_Gqz0d5oI2KodWt2_YB6RPX8_TtdR-Y_0-oiv0fAPwNAE9VG1_63_3EdXO32z5C2gL8B1uT8JrgyWQ2fXdwCR2GQvfnx9dskybLgNcxTOghymMSwCAOo8t0C7tEogq_GRQhf0mxM96IABrM0iYO4gDRNs4QO9CkePHhsHTyBNB7CYTLVVmlI8wCOpvGgnSGc3wbTc_naTbA-P5nLOwAKoXI3ZHLHYwJz165wLbVLhGsJh2GyBZ72fi55N3Bd634cl21lHSkVKEoNitLytsDOyvi0nTPyd7PtHg1lRzaL8hcU7v778UNwOSwmURmN4_17YAPp8pzmQGkbrC_PPsr74BL_tHy7OHvQ4BqCw_MGzk_QoC6H
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwELZKixA98F9RKOBDkQApNHGcODkg5O5mlVXTJEqyZakqhfgnEgW2pbuAuPEOfRsehyfBzs8CEuLWA-eMIiXzzYxnPPMNANu2K1zNsmk4EqsExap85QcZMiqBHY5r4pt1o-mIxLE3nfrpCvjez8LotsreJzaOWpxwXSPf0ROWeirLs3fqri0iHY5enn409AYpfdPar9NoIbInv35R6dv8xXiodP0YoVFQDEKj2zBgcIu4C8Plpl8RU2LGsC89z5WOqBhGjHOzklhZs7Rs4un9NJVDaiFtVDuI1baohPQYttV7L4E1glVQbNoG82UUUAeP9nYbEUPZsNnNBmq66tmHY91T5j_Xm0Z-j4Z_BoMmwo2u_8__5ga41p2rIW0N4SZYkbNbYH1_SUo7vw3ehUF2-OPb-X6SZcFrmKd0EOQwiWERBlDlwQXcpVEEX42LEB7QbEx3owAG0zSJg7iANE2zhA50dQ8ePbGOnkIaD-EwmWipNKR5AEeTeNByC-d3wORCvnYDrM5OZvIugEKonA6Z3PGYwNy1K1xLrR7hWsJhmGyCZ73OS94Rset9IO_LtuOOlAogpQZIaXmbYHspfNryj_xdbKtHRtk5oXn5Cxb3_v34Ebii8FJG43jvPriKdNdOU2faAquLs0_yAbjMPy_ezs8eNhCH4M1F4-Yn4vc3Tg
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=HERZ%E2%80%93MORREY+SPACES+ON+THE+UNIT+BALL+WITH+VARIABLE+EXPONENT+APPROACHING+%5C%281%5C%29+AND+DOUBLE+PHASE+FUNCTIONALS&rft.jtitle=Nagoya+mathematical+journal&rft.au=Mizuta%2C+Yoshihiro&rft.au=Ohno%2C+Takao&rft.au=Shimomura%2C+Tetsu&rft.date=2021-06-01&rft.pub=Cambridge+University+Press&rft.issn=0027-7630&rft.eissn=2152-6842&rft.volume=242&rft.spage=1&rft.epage=34&rft_id=info:doi/10.1017%2Fnmj.2019.18&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0027-7630&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0027-7630&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0027-7630&client=summon