Results 11 to 20 of about 45 (44)

Pseudodifferential operators with homogeneous symbols.

Michigan Mathematical Journal, 1999
We prove boundedness of pseudodifferential operators with symbols satisfying the conditions j@ fi ¸ @ fl x a(x; ¸)j C fi;fl j¸j m\Gammajfij+jflj on homogeneous Besov-Lipschitz and Triebel-Lizorkin spaces 1 Introduction The study of ...
Loukas Grafakos, Rodolfo H Torres
exaly   +1 more source

Some estimates for commutators of bilinear pseudo-differential operators

Open Mathematics, 2022
We obtain a class of commutators of bilinear pseudo-differential operators on products of Hardy spaces by applying the accurate estimates of the Hörmander class. And we also prove another version of these types of commutators on Herz-type spaces.
Yang Yanqi, Tao Shuangping
doaj   +1 more source

Notes on pseudodifferential operators commutators and Lipschitz functions

Open Mathematics, 2023
This article focuses on the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions and obtains a sufficient condition such that these operators are bounded from Lp(Rn){L}^{p}\left({{\bf{R}}}^{n}) into the ...
Deng Yu-long
doaj   +1 more source

ON THE GEOMETRY OF Dif f (S 1 )−PSEUDODIFFERENTIAL OPERATORS BASED ON RENORMALIZED TRACES

, 2021
International audienceIn this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of Dif f (S 1) with a group of classical pseudo-differential operators of any order. Several subgroups are considered ,
Magnot, Jean-Pierre
core   +1 more source

Functions of self‐adjoint operators in ideals of compact operators

Journal of the London Mathematical Society, Volume 95, Issue 1, Page 157-176, February 2017., 2017
Abstract For self‐adjoint operators A,B, a bounded operator J, and a function f:R→C, we obtain bounds in quasi‐normed ideals of compact operators for the difference f(A)J−Jf(B) in terms of the operator AJ−JB. The focus is on functions f that are smooth everywhere except for finitely many points. A typical example is the function f(t)=|t|γ with γ∈(0,1).
Alexander V. Sobolev
wiley   +1 more source

Atomic, molecular and wavelet decomposition of generalized 2‐microlocal Besov spaces

Journal of Function Spaces, Volume 8, Issue 2, Page 129-165, 2010., 2010
We introduce generalized 2‐microlocal Besov spaces and give characterizations in decomposition spaces by atoms, molecules and wavelets. We apply the wavelet decomposition to prove that the 2‐microlocal spaces are invariant under the action of pseudodifferential operators of order 0.
Henning Kempka, Hans Triebel
wiley   +1 more source

Domains of pseudo‐differential operators: a case for the Triebel‐Lizorkin spaces

Journal of Function Spaces, Volume 3, Issue 3, Page 263-286, 2005., 2005
The main result is that every pseudo‐differential operator of type 1, 1 and order d is continuous from the Triebel‐Lizorkin space Fp,1d to Lp, 1 ≤ p≺∞, and that this is optimal within the Besov and Triebel‐Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander′s condition on the twisted ...
Jon Johnsen, Victor Burenkov
wiley   +1 more source

The pseudodifferential operator A(x, D)

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 8, Page 407-419, 2004., 2004
The pseudodifferential operator (p.d.o.) A(x, D), associated with the Bessel operator d2/dx2 + (1 − 4μ2)/4x2, is defined. Symbol class Hρ,δm is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space Hμ into itself. An integral representation of p.d.o.
R. S. Pathak, S. Pathak
wiley   +1 more source

Relativistic wave equations with fractional derivatives and pseudodifferential operators

Journal of Applied Mathematics, Volume 2, Issue 4, Page 163-197, 2002., 2002
We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator (□1/n). The equations corresponding to n = 1 and 2 (Klein‐Gordon and Dirac equations) are local in their nature, but the multicomponent equations for arbitrary n > 2 are nonlocal. We show the representation of the generalized
Petr Závada
wiley   +1 more source

Global solutions of semilinear heat equations in Hilbert spaces

Abstract and Applied Analysis, Volume 1, Issue 3, Page 263-276, 1996., 1996
The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one‐parameter strongly continuous semigroups of bounded linear operators.
G. Mihai Iancu, M. W. Wong
wiley   +1 more source