Atomic Decompositions of Localized Hardy Spaces with Variable Exponents and Applications

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Abstract

In this paper, we introduce the localized Hardy spaces with variable exponents \(h^{p(\cdot )}\) and establish a new atomic decomposition theorem for \(h^{p(\cdot )}\) by using the discrete Littlewood–Paley–Stein theory. As an application of atomic decomposition, we investigate molecule decomposition for \(h^{p(\cdot )}\). Moreover, pseudo-differential operators of order zero are shown to be bounded on \(h^{p(\cdot )}\).

Keywords

Atomic decomposition Localized Hardy space Variable exponent analysis Pseudo-differential operator Littlewood–Paley–Stein square function 

Mathematics Subject Classification

Primary 42B30 Secondary 42B25 42B35 46E30 

Notes

Acknowledgements

The project is sponsored by NUPTSF (Grant No.NY217151). The author also wishes to express his heartfelt thanks to the anonymous reviewer for corrections and so valuable suggestions.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.College of ScienceNanjing University of Posts and TelecommunicationsNanjingChina

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