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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 2, 1997, pp. 263–280
DOI: 10.4171/ZAA/763

Published online: 1997-06-30

Weighted Inequalities for the Fractional Maximal Operator in Lorentz Spaces via Atomic Decomposition of Tent Spaces

Y. Rakotondratsimba[1]

(1) Institut Polytechnique St. Louis, Cergy-Pontoise, France

Consider the usual fractional maximal operator $M_{\alpha}$ with $0 < \alpha < n$. A characterization of $\mathbb R^n$ weight functions $u(\cdot)$ and $\sigma(\cdot)$ for which $M_{\alpha}d\sigma$ sends the (generalized) Lorentz space $\Lambda^s_{\sigma}(w_1)$ into $\Lambda^r_u(w_2)$ with $1 < s < r < \infty$ is obtained by using a suitable-atomic decomposition of tent spaces.

Keywords: Weighted inequalities, maximal operators, tent spaces, Lorentz spaces

Rakotondratsimba Y.: Weighted Inequalities for the Fractional Maximal Operator in Lorentz Spaces via Atomic Decomposition of Tent Spaces. Z. Anal. Anwend. 16 (1997), 263-280. doi: 10.4171/ZAA/763