Moscow Mathematical Journal

Volume 25, Issue 4, October–December 2025 pp. 535–555.

Sobolev–Jawerth Embedding and Boundedness of Fractional Integral Operator on Weighted Triebel–Lizorkin–Morrey–Lorentz Spaces

Authors: Hongliang Li (1)
Author institution:(1) Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, China

Summary:

In this paper, we get a Sobolev–Jawerth embedding for weighted Triebel–Lizorkin–Morrey–Lorentz spaces by the theories of indices of the weighted Lorentz spaces and Littlewood–Paley spaces. Based on this result, the boundedness of the fractional integral operator on weighted Triebel–Lizorkin–Morrey–Lorentz spaces and weighted Hardy–Morrey–Lorentz spaces are established. Specifying the weights we recover the existing results as well as we acquire new results in the new and old settings.

2020 Math. Subj. Class. 46E30, 46B42.

Keywords: Weighted Lorentz space, weighted Triebel–Lizorkin–Morrey–Lorentz spaces, fractional integral operator, Sobolev–Jawerth embedding, boundedness.

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