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 \(h^{p(\cdot )}\).
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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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Tan, J. Atomic Decompositions of Localized Hardy Spaces with Variable Exponents and Applications. J Geom Anal 29, 799–827 (2019). https://doi.org/10.1007/s12220-018-0019-1
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DOI: https://doi.org/10.1007/s12220-018-0019-1
Keywords
- Atomic decomposition
- Localized Hardy space
- Variable exponent analysis
- Pseudo-differential operator
- Littlewood–Paley–Stein square function