Banach Journal of Mathematical Analysis

Local Hardy--Littlewood maximal operator in variable Lebesgue spaces

A. Danelia, A. Gogatishvili, and T. Kopaliani

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We investigate the class $\mathcal{B}^{loc}(\mathbb{R}^{n})$ of exponents $p(\cdot)$ for which the local Hardy-Littlewood maximal operator is bounded in variable exponent Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^{n})$. Littlewood-Paley square function characterization of $L^{p(\cdot)}(\mathbb{R}^{n})$ spaces with the above class of exponent are also obtained.

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Banach J. Math. Anal., Volume 8, Number 2 (2014), 229-244.

First available in Project Euclid: 4 April 2014

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Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Variable exponent Lebesgue space local Hardy-Littlewood maximal function local Muckenhoupt classes, Littlewood-Paley theory square function


Gogatishvili, A.; Danelia, A.; Kopaliani, T. Local Hardy--Littlewood maximal operator in variable Lebesgue spaces. Banach J. Math. Anal. 8 (2014), no. 2, 229--244. doi:10.15352/bjma/1396640066.

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