{"paper":{"title":"On Nikol'skii inequalities for domains in $R^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Prymak, Z. Ditzian","submitted_at":"2014-09-18T18:23:34Z","abstract_excerpt":"Nikol'skii inequalities for various sets of functions, domains and weights will be discussed. Much of the work is dedicated to the class of algebraic polynomials of total degree $n$ on a bounded convex domain $D$. That is, we study $\\sigma:= \\sigma(D,d)$ for which \\[ \\|P\\|_{L_q(D)}\\le c n^{\\sigma(\\frac1p-\\frac1q)}\\|P\\|_{L_p(D)},\\quad 0<p\\le q\\le\\infty, \\] where $P$ is a polynomial of total degree $n$. We use geometric properties of the boundary of $D$ to determine $\\sigma(D,n)$ with the aid of comparison between domains. Computing the asymptotics of the Christoffel function of various domains "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5397","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}