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- W2949879077 abstract "This paper studies the following weighted, fractional Bernstein inequality for spherical polynomials on $sph$: begin{equation}label{4-1-TD-ab} |(-Delta_0)^{r/2} f|_{p,w}leq C_w n^{r} |f|_{p,w}, forall fin Pi_n^d, end{equation} where $Pi_n^d$ denotes the space of all spherical polynomials of degree at most $n$ on $sph$, and $(-Delta_0)^{r/2}$ is the fractional Laplacian-Beltrami operator on $sph$. A new class of doubling weights with conditions weaker than the $A_p$ is introduced, and used to fully characterize those doubling weights $w$ on $sph$ for which the weighted Bernstein inequality eqref{4-1-TD-ab} holds for some $1leq pleq infty$ and all $r>tau$. In the unweighted case, it is shown that if $0<p<infty$ and $r>0$ is not an even integer, then eqref{4-1-TD-ab} with $wequiv 1$ holds if and only if $r>(d-1)(f 1p-1)$. As applications, we show that any function $fin L_p(sph)$ with $0<p<1$ can be approximated by the de la Vall'ee Poussin means of a Fourier-Laplace series, and establish a sharp Sobolev type Embedding theorem for the weighted Besov spaces with respect to general doubling weights." @default.
- W2949879077 created "2019-06-27" @default.
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- W2949879077 date "2013-06-30" @default.
- W2949879077 modified "2023-10-14" @default.
- W2949879077 title "Weighted Fractional Bernstein's inequalities and their applications" @default.
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- W2949879077 doi "https://doi.org/10.48550/arxiv.1307.0207" @default.
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