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- W4287725536 abstract "It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate. While these inequalities are optimal for general functions of bounded mean oscillation, the main result of this paper is an improvement for functions in a class of critical Sobolev spaces. Precisely, we prove the inequality [mathcal{H}^{beta}_{infty}({xin Omega:|I_alpha f(x)|>t})leq Ce^{-ct^{q'}}] for all $|f|_{L^{N/alpha,q}(Omega)}leq 1$ and any $beta in (0,N]$, where $Omega subset mathbb{R}^N$, $mathcal{H}^{beta}_{infty}$ is the Hausdorff content, $L^{N/alpha,q}(Omega)$ is a Lorentz space with $q in (1,infty]$, $q'=q/(q-1)$ is the Holder conjugate to $q$, and $I_alpha f$ denotes the Riesz potential of $f$ of order $alpha in (0,N)$." @default.
- W4287725536 created "2022-07-26" @default.
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- W4287725536 date "2020-07-09" @default.
- W4287725536 modified "2023-09-29" @default.
- W4287725536 title "An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces" @default.
- W4287725536 doi "https://doi.org/10.48550/arxiv.2007.04576" @default.
- W4287725536 hasPublicationYear "2020" @default.
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