1,720,974 research outputs found
Lp microlocal properties for vector weighted pseudodifferential operators with smooth symbols
No full textThe authors introduce a class of pseudodifferential operators, whose symbols satisfy completely inhomogeneous estimates at infinity for the derivatives. Continuity properties in suitable weighted Sobolev spaces of Lp type are given and Lp microlocal properties studied
L p continuity and microlocal properties for pseudodifferential operators
No full textThe aim of this paper is to give a brief survey about L p continuity and microlocal regularity for classical pseudodifferential operators, with p≠ 2. In particular, we focus on some classes of operators with smooth symbol satisfying decay properties of quasi-homogeneous or completely non-homogeneous type
Microlocal regularity of Besov type for solutions to quasi-elliptic nonlinear partial differential equations
No full textUsing a standard linearization technique and previously obtained microlocal properties for pseudodifferential operators with smooth coefficients, the authors state results of microlocal regularity in generalized Besov spaces for solutions to nonlinear PDE
Pseudodifferential operators on time-frequency invariant Banach spaces and applications to Gabor Frames
No full textStarting from the study of pseudodifferential operators with completely periodic symbols, we obtain results of continuity and invertibility of a class of Gabor operators on time-frequency invariant Banach spaces. As an application, we find sufficient conditions for the existence of Gabor frames on L^2, associated with a general lattice LZ^{2d}, where L is an invertible square matrix
Pseudodifferential operators with completely periodic symbols
No full textMotivated by the recent paper of Boggiatto-Garello (J Pseudo-Differ Oper Appl 11:93-117, 2020) where a Gabor operator is regarded as pseudodifferential operator with symbol p(x, \omega) periodic on both the variables, we study the continuity and invertibility, on general time frequency invariant spaces, of pseudodifferential operators with completely periodic symbol and general t quantization
L^p continuity for pseudodifferential operators
No full textThe authors give a short survey about the LP-continuity of pseudo-differential operators both with smooth and non-smooth symbols
Regularity for quasi-elliptic pseudo-differential operators with symbols in Holder classes
No full textAfter proving a result of continuity for pseudo-differential operators whose symbols belong to Holder spaces and satisfy a decay of quasi-homogeneous type, the authors construct a suitable symbolic calculus and a parametrix for quasi-elliptic operators; these tools are applied to the study of quasi-elliptic linear partial differential equations with Holder coefficients
Continuity in quasi-homogeneous Sobolev spaces for pseudo-differential operators with Besov symbols
No full textIn this paper a result of continuity for pseudo-differential operators With non-regular symbols on spaces of quasi-homogeneous type is given. More precisely, the symbols a(x, xi) take their values in a quasi-homogeneous Besov space with respect to the x variable; moreover a finite number of derivatives With respect to the second variable satisfies, in Besov norm, decay estimates of quasi-homogeneous type
Microlocal regularity of nonlinear PDE in quasi-homogeneous Fourier–Lebesgue spaces
Get PDFWe study the continuity in weighted Fourier–Lebesgue spaces for a class of pseudodifferential operators, whose symbol has finite Fourier–Lebesgue regularity with respect to x and satisfies a quasi-homogeneous decay of derivatives with respect to the ξ variable. Applications to Fourier–Lebesgue microlocal regularity of linear and nonlinear partial differential equations are given
L^p microlocal properties for multi-quasi-elliptic pseudodifferential operators
Get PDFIn the present paper microlocal properties of a class of suitable Lp bounded pseudodifferential operators are stated in the framework of weighted Sobolev spaces of Lp type. Applications to microlocal regularity of solutions to multi-quasi-elliptic partial differential equations are also given
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