Commun. Korean Math. Soc.
Published online November 16, 2020
Bilel Selmi and Nina Svetova
Faculté des Sciences de Monastir, Petrozavodsk State University
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 $m$-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 : 28A12, 28A78, 28A80, 31E05
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