On Bernstein- and Marcinkiewicz-type inequalities on multivariate C^α-domains

04/05/2022

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by   Feng Dai, et al.

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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≤α≤ 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.