Projections and slices of measures
Commun. Korean Math. Soc. 2021 Vol. 36, No. 2, 327-342
Published online November 16, 2020
Printed April 30, 2021
Bilel Selmi, Nina Svetova
University of Monastir; Lenin str., 33, 185910, Petrozavodsk,
Abstract : We consider a generalization of the $L^q$-spectrum with respect to two Borel probability measures on $\mathbb{R}^n$ having the same compact support, and also study their behavior under orthogonal projections of measures onto an $m$-dimensional subspace. In particular, we try to improve the main result of Bahroun and Bhouri \cite{1}. In addition, we are interested in studying the behavior of the generalized lower and upper $L^q$-spectrum with respect to two measures on ``sliced'' measures in an $(n-m)$-dimensional linear subspace. The results in this article establish relations with the $L^q$-spectrum with respect to two Borel probability measures and its projections and generalize some well-known results.
Keywords : Orthogonal projection, dimension spectra, sections, convolutions
MSC numbers : Primary 28A78, 28A80
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