Estimates of \(L^p\)-oscillations of functions for \(p>0\)

DOI10.1134/S0001434615030098zbMath1319.42015MaRDI QIDQ2352587

V. G. Krotov, A. I. Porabkovich

Publication date: 3 July 2015

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

maximal operatorsPoincaré-Sobolev inequalities\(\theta\)-Lebesgue points\(L^p\)-oscillationsHajłasz-Sobolev classes

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (5)

On optimal Banach spaces containing a weight cone of monotone or quasiconcave functions ⋮ Unnamed Item ⋮ On the continuity of best approximations by constants on balls in metric measure spaces ⋮ Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). I: Lebesgue points ⋮ Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). II: Lusin's approximation

Cites Work

• Lectures on analysis on metric spaces
• Sobolev spaces on an arbitrary metric space
• Generalized Sobolev classes on metric measure spaces
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• \(H^p\) spaces of several variables
• Maximal Functions Measuring Smoothness
• Quantitative form of the Luzin C-property
• Sobolev type inequalities for p>0
• Sobolev met Poincaré
• Criteria for compactness inL^p-spaces,p≥ 0
• Estimates for singular integral operators in terms of maximal functions
• Estimates of maximal functions measuring local smoothness
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