Abstract: Let $M=G/H$ be a compact connected isotropy irreducible Riemannian homogeneous manifold, where is a compact Lie group (may be, disconnected) acting on $M$ by isometries. This class includes all compact irreducible Riemannian symmetric spaces and, for example, the tori $T^n=R^n/Z^n$ with the natural action on itself extended by the finite group generated by all permutations of the coordinates and inversions in circle factors. We say that $u$ is a polynomial on $M$ if it belongs to some $G$-invariant finite dimensional subspace $E$ of $L^2(M)$ . We compute or estimate from above the averages over the unit sphere $S$ in $E$ for some metric quantities such as Hausdorff measures of level set and norms in $L^p(M)$, $1\leq p\leq\infty$, where $M$ is equipped with the invariant probability measure. For example, the averages over $S$ of $\|u\|_{L^p(M)}, $p\geq2$, are less than \sqrt{\frac{p+1}{e}} independently of $M$ and $E$ .

Cite: Gichev V.M.
Metric properties in the mean of polynomials on compact isotropy irreducible homogeneous spaces
Analysis and Mathematical Physics. 2013. V.3. N2. P.119–144. DOI: 10.1007/s13324-012-0051-4 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Aug 27, 2012
Published online:	Nov 1, 2012

Identifiers:

Web of science:	WOS:000341585700002
Scopus:	2-s2.0-84937897276
Elibrary:	23981850
OpenAlex:	W2140660077

Citing:

DB	Citing
OpenAlex	5
Scopus	5
Web of science	4
Elibrary	8

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