Boundedness of Convolution Operators on Hardy Spaces

Establishing conditions for the boundedness of an operator taking Hp(Rn) into Lp(Rn) , with 0 < p≤ 1 , is a classical subject. A standard approach to such problems is using the atomic characterization of Hp(Rn) , 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. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.