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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 4 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1396640066

Digital Object Identifier
doi:10.15352/bjma/1396640066

Mathematical Reviews number (MathSciNet)
MR3189553

Zentralblatt MATH identifier
1285.42018

Subjects
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.)

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

Citation

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. https://projecteuclid.org/euclid.bjma/1396640066


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