Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach

DOI10.1007/978-0-387-85650-6_4zbMath1175.46020OpenAlexW1027619995MaRDI QIDQ3627652

Yuri A. Brudnyi

Publication date: 13 May 2009

Published in: Sobolev Spaces in Mathematics II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-85650-6_4

zbMATH Keywords

local polynomial approximationspaces of smooth functionsLuzin type theorems

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Approximation by polynomials (41A10)

Related Items (7)

Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space ⋮ Interpolation of Morrey-Campanato and related smoothness spaces ⋮ Calderón-Zygmund operators in Morrey spaces ⋮ Entropy numbers in function spaces with mixed integrability ⋮ Characterization of traces of smooth functions on Ahlfors regular sets ⋮ On the Banach structure of multivariate BV spaces ⋮ Morrey spaces, their duals and preduals

Cites Work

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• On functions of bounded mean oscillation
• Maximal functions measuring smoothness
• On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.
• Metric spaces with linear extensions preserving Lipschitz condition
• Poisson Integrals of Regular Functions
• Weakly Differentiable Functions
• Sobolev type inequalities for p>0
• Nonlinear approximation and the space BV[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]
• Best Approximations in L 1 are Near Best in L p , p < 1
• PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
• Estimates for singular integral operators in terms of maximal functions
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)
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