On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^α$-domains
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917962182557696 |
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| author | Dai, Feng Kroó, András Prymak, Andriy |
| author_facet | Dai, Feng Kroó, András Prymak, Andriy |
| contents | We prove new Bernstein and Markov type inequalities in $L^p$ spaces associated with the normal and the tangential derivatives on the boundary of a general compact $C^α$-domain with $1\leq α\leq 2$. These estimates are also applied to establish Marcinkiewicz type inequalities for discretization of $L^p$ norms of algebraic polynomials on $C^α$-domains with asymptotically optimal number of function samples used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02349 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^α$-domains Dai, Feng Kroó, András Prymak, Andriy Numerical Analysis Classical Analysis and ODEs 41A17, 41A10, 42C05, 46N10, 42B99 We prove new Bernstein and Markov type inequalities in $L^p$ spaces associated with the normal and the tangential derivatives on the boundary of a general compact $C^α$-domain with $1\leq α\leq 2$. These estimates are also applied to establish Marcinkiewicz type inequalities for discretization of $L^p$ norms of algebraic polynomials on $C^α$-domains with asymptotically optimal number of function samples used. |
| title | On Bernstein- and Marcinkiewicz-type inequalities on multivariate $C^α$-domains |
| topic | Numerical Analysis Classical Analysis and ODEs 41A17, 41A10, 42C05, 46N10, 42B99 |
| url | https://arxiv.org/abs/2204.02349 |