Weighted estimates for time-fractional parabolic equations with VMO coefficients

2024/12/27 by He, Jia Wei, Tao, Lu Lu · 1 citation
#26A33 #34A12 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.19600

Abstract

This paper is devoted to the weighted estimates and the solvability of time-fractional parabolic equations. The leading coefficients \(a^ij(t,x)\) are assumed to have small mean oscillations in \((t,x)\) locally, in both non-divergence and divergence forms, in the whole space. By employing appropriate odd and even extensions along with suitable boundary value conditions, we derive the corresponding results for the half-space. The proofs rely on the application of the Fefferman-Stein theorem and the Hardy-Littlewood maximal function theorem in the context of weighted mixed spaces.

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• Muckenhoupt-weighted L_q(L_p) boundedness for time-space fractional nonlocal operators

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