| Abstract: |
| There has been growing interest in non-local operators in both analysis and probability. In particular, the structure of jumping kernels is closely connected to L\`evy processes, with the fractional Laplacian serving as the most fundamental example. In this presentation, we consider the boundedness of the non-local operators having variable coefficients in weighted Lebesgue spaces. We also provide some applications such as regularity theory of evolution equations and elliptic-type equations in weighted Lebesgue spaces and Krylov-type estimate for the processes generating our operators. |
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