An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

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It 6 Piece Modular Sectional 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 ARTHRI-PLUS SPRAY paper is an improvement for functions in a class of critical Sobolev spaces.Precisely, we prove the inequality.