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arXiv · 2608.01722

On Weighted Local Morrey-type and Complementary Local Morrey-Type Spaces

Amiran Gogatishvili·Yoshihiro Sawano·Tuğçe Ünver
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Abstract

In this paper, we establish necessary and sufficient conditions for continuous embeddings between weighted local Morrey-type spaces and weighted complementary local Morrey-type spaces. Rather than relying on standard multidimensional approaches, our methodology is based on a one-dimensional reduction. Specifically, we reduce the multidimensional embedding problems to corresponding weighted inequalities involving one-dimensional Ces\`{a}ro and Copson function spaces. Applying this reduction alongside recent results in the characterization of the embeddings between Ces\`{a}ro and Copson spaces, we provide complete characterizations for the embeddings \[ \LM_{p_1,q_1}(v_1, w_1) \hookrightarrow \LM_{p_2,q_2}(v_2, w_2)\] and \[\dual\LM_{p_1,q_1}(v_1, w_1) \hookrightarrow \LM_{p_2,q_2}(v_2, w_2).\] Our results cover all possible finite cases of the parameters $0 < p_1, p_2, q_1, q_2 < \infty$.

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Amiran Gogatishvili, Yoshihiro Sawano, Tuğçe Ünver. 2026-08-03. On Weighted Local Morrey-type and Complementary Local Morrey-Type Spaces. https://arxiv.org/abs/2608.01722

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