Boundedness of Convolution Operators on Hardy Spaces - Belinsky, Eduard; Liflyand, Elijah (Computational methods and function theory, 2019)
Establishing conditions for the boundedness of an operator taking H p ( R n ) into L p ( R n ) , with 0 < p ≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of H p ( R n ) , 0 < p ≤ 1 , and working with atoms. Unlike in certain earlier work on the subject we apply this machinery not to specific operators but to a wide general family of multivariate linear means generated by a multiplier. We illustrate the use of these new conditions applying them to some methods known from before.