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

  • Y. Rakotondratsimba

    Institut Polytechnique St. Louis, Cergy-Pontoise, France

Abstract

Consider the usual fractional maximal operator MαM_{\alpha} with 0<α<n0 < \alpha < n. A characterization of Rn\mathbb R^n weight functions u()u(\cdot) and σ()\sigma(\cdot) for which MαdσM_{\alpha}d\sigma sends the (generalized) Lorentz space Λσs(w1)\Lambda^s_{\sigma}(w_1) into Λur(w2)\Lambda^r_u(w_2) with 1<s<r<1 < s < r < \infty is obtained by using a suitable-atomic decomposition of tent spaces.

Cite this article

Y. Rakotondratsimba, Weighted Inequalities for the Fractional Maximal Operator in Lorentz Spaces via Atomic Decomposition of Tent Spaces. Z. Anal. Anwend. 16 (1997), no. 2, pp. 263–280

DOI 10.4171/ZAA/763