Weighted inequalities of Hardy type

DOI10.1007/BF01054210zbMath0729.42007MaRDI QIDQ805973

Eh. N. Batuev, Vladimir D. Stepanov

Publication date: 1989

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

zbMATH Keywords

wave equationboundednessCauchy problemmaximal Hardy-Littlewood operator in weighted spacesMuckenhoupt's theoremSteklov operatorsweighted Hardy inequalities for integration operators

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) A priori estimates in context of PDEs (35B45) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (25)

Hardy-Steklov operators and Sobolev-type embedding inequalities ⋮ Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis ⋮ Hardy type inequalities for fractional integrals and derivatives of Riemann-Liouville ⋮ Sharper and finer energy decay rate for an elastic string with localized Kelvin-Voigt damping ⋮ Sharp decay rates of degenerate hyperbolic-parabolic coupled system: rectangular domain vs one-dimensional domain ⋮ Some characterizations of dynamic weighted Hardy-type inequalities with applications ⋮ Stabilization for Wave Equation with Localized Kelvin–Voigt Damping on Cuboidal Domain: A Degenerate Case ⋮ Kolmogorov widths of weighted Sobolev classes on closed intervals ⋮ Widths of weighted Sobolev classes on a closed interval and the spectra of nonlinear differential equations ⋮ Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights ⋮ Characterizations of reverse dynamic weighted Hardy-type inequalities with kernels on time scales ⋮ Boundedness and compactness in weighted Lebesgue spaces of integral operators with variable integration limits ⋮ Boundedness criteria for the Hardy-Steklov operator expressed in terms of a fairway function ⋮ On a Hilbert-type inequality with the kernel involving extended Hardy operator ⋮ \(L_{p,q}\)-cohomology of some warped cylinders ⋮ BOUNDEDNESS AND COMPACTNESS OF A CERTAIN CLASS OF MATRIX OPERATORS WITH VARIABLE LIMITS OF SUMMATION ⋮ Two weighted norm dynamic inequalities with applications on second order half-linear dynamic equations ⋮ Integral operators with two variable integration limits on the cone of monotone functions ⋮ Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space ⋮ \(L _{p,q} \)-cohomology of warped cylinders ⋮ Hardy-type operators with general kernels and characterizations of dynamic weighted inequalities ⋮ Kolmogorov widths and approximation numbers of Sobolev classes with singular weights ⋮ Explicit decay rate for a degenerate hyperbolic-parabolic coupled system ⋮ Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights. II ⋮ Boundedness of Riemann-Liouville operator from weighted Sobolev space to weighted Lebesgue space for 1 < q < p < ∞

Cites Work

• Hardy's inequality and its extensions
• Generalized Hardy's inequality
• Hardy Inequalities with Mixed Norms
• Osservazioni sopra una classe di disuguaglianze
• Hardy's inequality with weights
• Weighted Norm Inequalities for the Hardy Maximal Function
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