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- W4313643569 abstract "We prove the boundedness of the non-local operator $$begin{aligned} mathcal {L}^a u(x)=int _{mathbb {R}^d} left( u(x+y)-u(x)-chi _alpha (y)big (nabla u(x),ybig )right) a(x,y)frac{dy}{|y|^{d+alpha }} end{aligned}$$ from $$H_{p,w}^alpha (mathbb {R}^d)$$ to $$L_{p,w}(mathbb {R}^d)$$ for the whole range of $$p in (1,infty )$$ , where w is a Muckenhoupt weight. The coefficient a(x, y) is bounded, merely measurable in y, and Hölder continuous in x with an arbitrarily small exponent. We extend the previous results by removing the largeness assumption on p as well as considering weighted spaces with Muckenhoupt weights. Using the boundedness result, we prove the unique solvability in $$L_p$$ spaces of the corresponding parabolic and elliptic non-local equations." @default.
- W4313643569 created "2023-01-07" @default.
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- W4313643569 date "2023-01-07" @default.
- W4313643569 modified "2023-10-01" @default.
- W4313643569 title "Boundedness of non-local operators with spatially dependent coefficients and $$L_p$$-estimates for non-local equations" @default.
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- W4313643569 doi "https://doi.org/10.1007/s00526-022-02392-4" @default.
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