Pointwise estimates for rough operators with applications to Sobolev inequalities

Published 19 Jul 2023 in math.CA | (2307.10417v2)

Abstract: We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities with an operator on the left-hand side.

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