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Wavelet characterizations of variable Hardy-Lorentz spaces

Yao He
대한수학회 (The Korean Mathematical Society)|2024.03|대한수학회보 (Bulletin of the KMS)|제61권 제2호|pp. 489-509|DOI 10.4134/BKMS.b230191

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참고문헌

키워드

atomwaveletVariable Hardy-Lorentz spacePeetre-type maximal functionLittlewood-Paley $g$-function
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초록

In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\R^{n})$ in terms of wavelets.

Abstract

In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\R^{n})$ in terms of wavelets.

참고문헌 (26)

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