$L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866912322509864960 |
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| author | Dai, Feng Prymak, Andriy |
| author_facet | Dai, Feng Prymak, Andriy |
| contents | We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm and positive cubature formula. Both results are optimal in the sense that the number of function samples used has the order of the dimension of the corresponding space of algebraic polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_06728 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization Dai, Feng Prymak, Andriy Classical Analysis and ODEs Numerical Analysis 42C05, 46N10, 42B99 We prove a new Bernstein type inequality in $L^p$ spaces associated with the tangential derivatives on the boundary of a general compact $C^2$-domain. We give two applications: Marcinkiewicz type inequality for discretization of $L^p$ norm and positive cubature formula. Both results are optimal in the sense that the number of function samples used has the order of the dimension of the corresponding space of algebraic polynomials. |
| title | $L^p$-Bernstein inequalities on $C^2$-domains and applications to discretization |
| topic | Classical Analysis and ODEs Numerical Analysis 42C05, 46N10, 42B99 |
| url | https://arxiv.org/abs/2010.06728 |