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arXiv · 2307.16323

Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces

Marcos Bonich·Daniel Carando·Martín Mazzitelli
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Abstract

We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear operator $T\colon L^{q(\cdot)}(Ω_2, μ)\to L^{p(\cdot)}(Ω_1, ν)$ has a bounded $\ell^r$-valued extension. We consider both non-atomic measures and measures with atoms and show the differences that can arise. We present some applications of our results to weighted norm inequalities of linear operators and vector-valued extensions of fractional operators with rough kernel.

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Marcos Bonich, Daniel Carando, Martín Mazzitelli. 2024-10-10. Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces. https://doi.org/10.1007/s43037-024-00344-y

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