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Maximal Operators and Characterization of Hardy Spaces

Abstract

It is known that the maximal operator σ* ƒ is of type (Hp,Lp) if the Vilenkin group G is bounded and \(p > \tfrac{1}{2}\). We prove a maximal converse inequality which characterizes the space Hp by means of the operator σƒ:= supn |σMnƒ|, for bounded groups.

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Acknowledgement

The authors would like to thank the referees for their valuable remarks and suggestions.

Author information

Correspondence to N. Memić.

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Memić, N., Sadiković, S. Maximal Operators and Characterization of Hardy Spaces. Anal Math 46, 119–131 (2020). https://doi.org/10.1007/s10476-020-0021-2

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Key words and phrases

  • Vilenkin group
  • Hardy space
  • maximal operator

Mathematics Subject Classification

  • 42C10