Weighted Sobolev Spaces and Pseudodifferential Operators with Smooth Symbols

DOI10.2307/1998595zbMath0482.35082OpenAlexW4243345926MaRDI QIDQ3940227

Nicholas Stuart Miller

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1998595

zbMATH Keywords

Hardy-Littlewood maximal operatorpseudodifferential operator of order O

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Related Items (49)

Weighted estimates for Toeplitz operators related to pseudodifferential operators ⋮ Sharp function and weighted \(L^ p\) estimates for a class of pseudo- differential operators ⋮ Toeplitz-type operators associated to pseudodifferential operators ⋮ Weighted boundedness of multilinear pseudo-differential operators ⋮ Multipliers spaces, Muckenhoupt weights and pseudo-differential operators ⋮ Boundedness of Toeplitz Type Operators Associated to Fractional and Pseudo-Differential Operators on Orlicz Space ⋮ New weighted norm inequalities for pseudodifferential operators and their commutators ⋮ The weighted \(L^ p\)-boundedness of product-type pseudodifferential operators ⋮ Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces ⋮ Pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces ⋮ Extrapolation of compactness on weighted spaces ⋮ On the Kato problem and extensions for degenerate elliptic operators ⋮ Sparse bounds for pseudo-multipliers associated to Grushin operators. I. ⋮ Weighted maximal \(L_q (L_p)\)-regularity theory for time-fractional diffusion-wave equations with variable coefficients ⋮ Hölder continuity of weak solutions to nonlocal Schrödinger equations with \(A_1\)-Muckenhoupt potentials ⋮ A weighted \(L_p\)-regularity theory for parabolic partial differential equations with time-measurable pseudo-differential operators ⋮ A pointwise estimate for pseudo-differential operators ⋮ A remark related pseudo-differential operators on multi-parameter Besov-Lipschitz and Triebel-Lizorkin spaces ⋮ Removable singularities for subsolutions of elliptic equations involving weighted variable exponent Sobolev spaces ⋮ Sharp function estimates for bilinear pseudo-differential operators ⋮ Sharp maximal function inequalities and boundedness for Toeplitz type operator associated to pseudo-differential operator ⋮ The compactly supported wavelet characterization of non-homogeneous Herz-Sobolev spaces with variable exponent ⋮ Sparse bounds for pseudo-multipliers associated to Grushin operators. II ⋮ Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces ⋮ Toward weighted Lorentz-Sobolev capacities from Caffarelli-Silvestre extensions ⋮ Boundedness of a class of sublinear operators and their commutators on generalized Morrey spaces ⋮ Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space ⋮ Elliptic equations of higher-order in weighted Sobolev spaces ⋮ Weighted variable Sobolev spaces and capacity ⋮ The hydromechanical equilibrium state of poroelastic media with a static fracture: A dimension-reduced model with existence results in weighted Sobolev spaces and simulations with an XFEM discretization ⋮ Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutators ⋮ Control of pseudodifferential operators by maximal functions via weighted inequalities ⋮ Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes ⋮ Mean oscillation and boundedness of Toeplitz type operators associated to pseudo-differential operators ⋮ \(L_{\alpha }^p\)-boundedness of the pseudo-differential operators associated with the Kontorovich-Lebedev transform ⋮ Removable singularities for div v=f in weighted Lebesgue spaces ⋮ Global and local regularity of Fourier integral operators on weighted and unweighted spaces ⋮ Operators of harmonic analysis in weighted spaces with non-standard growth ⋮ Weak and strong type estimates for the multilinear pseudo-differential operators ⋮ Pseudodifferential operators on weighted Hardy spaces ⋮ Characterization of the traces on the boundary of functions in magnetic Sobolev spaces ⋮ Compactness of commutators of pseudo-differential operators with smooth symbols on weighted Lebesgue spaces ⋮ The Kato problem for operators with weighted ellipticity ⋮ On weighted norm inequalities for oscillatory integral operators ⋮ Double weighted commutators theorem for pseudo-differential operators with smooth symbols ⋮ Local sharp maximal functions ⋮ Weighted estimates of singular integrals and their applications ⋮ A Commutator Estimate for Pseudo-Differential Operators ⋮ Boundedness of Pseudodifferential Operators on Banach Function Spaces

Cites Work

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• \(H^p\) spaces of several variables
• Weighted norm inequalities for maximal functions and singular integrals
• A Class of L p -Bounded Pseudo-Differential Operators
• Weighted Norm Inequalities for the Hardy Maximal Function
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform

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