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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.
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참고문헌 (42)
참고문헌 신청
Najmeddine Attia / 2019 / Relative multifractal box-dimensions / Filomat 33(9):2841~2859
N. Attia / 2020 / On the Billingsley dimension of Birkhoff average in the countable symbolic space / Comptes Rendus Math 358:255~265
N. Attia / 2017 / Some density results of relative multifractal analysis / Chaos, Solitons & Fractals 103:1~11
F. Bahroun / 2006 / Multifractals and projections / Extracta Math 21(1):83~91
J. Barral / 2011 / Multifractal analysis for projections of Gibbs and related measures / Ergodic Theory Dynam. Systems 31(3,):673~701
N. Attia / 2020 / On the Billingsley dimension of Birkhoff average in the countable symbolic space / Comptes Rendus Math 358:255~265
N. Attia / 2017 / Some density results of relative multifractal analysis / Chaos, Solitons & Fractals 103:1~11
F. Bahroun / 2006 / Multifractals and projections / Extracta Math 21(1):83~91
J. Barral / 2011 / Multifractal analysis for projections of Gibbs and related measures / Ergodic Theory Dynam. Systems 31(3,):673~701
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