Author: Rodolfo Humberto TorresPublisher:
ISBN:
Category : Decomposition method
Languages : en
Pages : 172
Book Description
Boundedness Results for Operators with Single Kernels on Distribution Spaces
Author: Rodolfo Humberto TorresPublisher:
ISBN:
Category : Decomposition method
Languages : en
Pages : 172
Book Description
Boundedness Results for Operators with Singular Kernels on Distribution Spaces
Author: Rodolfo Humberto TorresPublisher:
ISBN: 9781470408688
Category : Decomposition method
Languages : en
Pages : 172
Book Description
Boundedness Results for Operators with Singular Kernels on Distribution Spaces
Author: Rodolfo Humberto TorresPublisher: American Mathematical Soc.
ISBN: 0821825054
Category : Calderón-Zygmund operator
Languages : en
Pages : 185
Book Description
In this monograph, the author generalizes the T1 theorem of G. David and J.-L. Journé to the context of Triebel-Lizorkin spaces, which include most of the function and distribution spaces of importance in classical analysis. M. Frazier and B. Jawerth have shown that these spaces admit decompositions in terms of certain fundamental building blocks, known as "smooth atoms'' and "smooth molecules''. In the author's words, "to prove that an operator is bounded on a Triebel-Lizorkin space, it is enough to show that it maps every family of smooth atoms into a family of smooth molecules''. The same basic techniques can be used to study operators between two different Triebel-Lizorkin spaces. Results are obtained for a wide variety of operators acting on the Triebel-Lizorkin spaces, including generalized Calderón-Zygmund operators and their derivatives; potential operators; fractional integral operators; and the Hörmander classes of pseudodifferential operators. When these general results are restricted to specific spaces, many classical boundedness results are recovered.
Boundedness Results for Operators with Singular Kernels on Distribution Spaces
Author: Rodolfo Humberto TorresPublisher: American Mathematical Soc.
ISBN: 9780821861653
Category : Mathematics
Languages : en
Pages : 190
Book Description
Discrete decomposition techniques for spaces for functions or distributions are very useful tools for studying many problems in analysis. In this work, the author uses this type of decomposition, associated with the so-called *p-transform and wavelet-transform theories, to analyse a large class of operators, including pseudodifferential operators, Calderon-Zygmund operators, and other operators with singular kernels. The methods used combine Littlewood-Paley type characterizations of spaces of distributions with certain atomic and molecular decompositions. In this way, the study of operators on most of the classical function spaces - such as Hardy spaces, Besov-Lipschitz spaces, and Sobolev spaces - can be accomplished in a unified manner. The book is written in an expository style that makes it suitable for advanced graduate students in analysis.
On the Boundedness of Certain Operators with Singular Kernels on Distribution Spaces
Author: Rodolfo Humberto TorresPublisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 344
Book Description
Fundamentals of Fourier Analysis
Author: Loukas GrafakosPublisher: Springer Nature
ISBN: 3031565002
Category :
Languages : en
Pages : 416
Book Description
On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb {R}^n$ and Related Estimates
Author: Pascal AuscherPublisher: American Mathematical Soc.
ISBN: 0821839411
Category : Mathematics
Languages : en
Pages : 102
Book Description
This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
Abstracts of Papers Presented to the American Mathematical Society
Author: American Mathematical SocietyPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 692
Book Description
Mathematical Reviews
Author: Time-Frequency Analysis of Operators
Author: Elena CorderoPublisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110530600
Category : Mathematics
Languages : en
Pages : 340
Book Description
This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.