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The Weyl correspondence as a functional calculus

100%
Alvarez J.
Banach Center Publications
|
2000
|
tom 53
|
nr 1
79-88
EN
The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.
2
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S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case

51%
Alvarez J., Guzmán-Partida M., Skórnik U.
Studia Mathematica
|
2003
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tom 156
|
nr 2
143-163
EN
We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S'-convolutions. We characterize those tempered distribution that are S'-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application of our results we prove that every integrable distribution on ℝⁿ has a harmonic extension to the upper half-space $ℝ₊^{n+1}$.
3
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Weighted estimates for commutators of linear operators

51%
Alvarez J., Bagby R. J., Kurtz D. S., Pérez C.
Studia Mathematica
|
1993
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tom 104
|
nr 2
195-209
EN
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^p$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
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