Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup - Mathematics > Functional AnalysisReportar como inadecuado




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Abstract: Under the standard assumptions on the variable exponent $px$ log- anddecay conditions, we give a characterization of the variable exponent Besselpotential space $\mathfrak B^\alphaL^{p\cdot}\mathbb R^n$ in terms of therate of convergence of the Poisson semigroup $P t$. We show that the existenceof the Riesz fractional derivative $\mathbb{D}^\al f$ in the space$L^{p\cdot} n$ is equivalent to the existence of the limit$\frac{1}{\ve^\al}I-P \ve^\al f$. In the pre-limiting case $\sup xpx<\frac{n}{\al}$ we show that the Bessel potential space is characterized bythe condition $\|I-P \ve^\al f\| {p\cdot}\leqq C \ve^\al$



Autor: Humberto Rafeiro, Stefan Samko

Fuente: https://arxiv.org/







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