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- W4385714553 abstract "We extend the theory of matrix weights to the variable Lebesgue spaces. The theory of matrix $mathcal{A}_p$ weights has attracted considerable attention beginning with the work of Nazarov, Treil, and Volberg in the 1990s. We extend this theory by generalizing the matrix $mathcal{A}_p$ condition to the variable exponent setting. We prove boundedness of the convolution operator $mathbf{f}mapsto phiast mathbf{F}$ for $phi in C_c^infty(Omega)$, and show that the approximate identity defined using $phi$ converges in matrix weighted, variable Lebesgue spaces $L^{p(cdot)}(W,Omega)$ for $W$ in matrix $mathcal{A}_{p(cdot)}$. Our approach to this problem is through averaging operators; these results are of interest in their own right. As an application of our work, we prove a version of the classical $H=W$ theorem for matrix weighted, variable exponent Sobolev spaces." @default.
- W4385714553 created "2023-08-10" @default.
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- W4385714553 date "2023-08-07" @default.
- W4385714553 modified "2023-09-23" @default.
- W4385714553 title "Convolution Operators in Matrix Weighted, Variable Lebesgue Spaces" @default.
- W4385714553 doi "https://doi.org/10.48550/arxiv.2308.03912" @default.
- W4385714553 hasPublicationYear "2023" @default.
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