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Generalized Lebesgue Points for Hajłasz Functions
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en
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12
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Journal of Function Spaces, Volume 2018
Abstract
Let X be a quasi-Banach function space over a doubling metric measure space P. Denote by αX the generalized upper Boyd index of X. We show that if αX<∞ and X has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Hajłasz function uṀs,X. Moreover, if αX<(Q+s)/Q, then quasievery point is a Lebesgue point of u. As an application we obtain Lebesgue type theorems for Lorentz-Hajłasz, Orlicz-Hajłasz, and variable exponent Hajłasz functions.
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Heikkinen, T 2018, 'Generalized Lebesgue Points for Hajłasz Functions', Journal of Function Spaces, vol. 2018, 5637042. https://doi.org/10.1155/2018/5637042