The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 799–827 | Cite as

Atomic Decompositions of Localized Hardy Spaces with Variable Exponents and Applications

  • Jian TanEmail author


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 \(h^{p(\cdot )}\).


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 



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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© Mathematica Josephina, Inc. 2018

Authors and Affiliations

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

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