Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

http://grupo.us.es/anaresba/trabajos/carlosperez/1preprint.pdf

New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

An introduction to orthogonal polynomials, by Theodore S. Chihara. Pp xii, 249. £26·30. 1978. SBN 0 677 04150 0 (Gordon and Breach)

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights

A net (x
 α
 ) in a vector lattice X is said to uo-converge to x if $$\left| {{x_\alpha } - x} \right| \wedge u\xrightarrow{o}0$$
 for every u ≥ 0. In the first part of this paper, we study some functional-analytic aspects of uo-convergence. We prove that uoconvergence is stable under passing to and from regular sublattices. This fact leads to numerous applications presented throughout the paper. In particular, it allows us to improve several results in [27, 26]. In the second part, we use uo-convergence to study convergence of Cesaro means in Banach lattices. In particular, we establish an intrinsic version of Komlos’ Theorem, which extends the main results of [35, 16, 31] in a uniform way. We also develop a new and unified approach to Banach–Saks properties and Banach–Saks operators based on uo-convergence. This approach yields, in particular, short direct proofs of several results in [20, 24, 25].

Uo-convergence and its applications to Cesàro means in Banach lattices

https://euler.us.es/~curbera/publications/AdvMath-203.pdf

Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals

Operators into L1 of a vector measure and applications to Banach lattices.

We present an extrapolation theory that allows us to obtain, from weighted L p inequalities on pairs of functions for p fixed and all A1 weights, es- timates for the same pairs on very general rearrangement invariant quasi-Banach function spaces with A1 weights and also modular inequalities with A1 weights. Vector-valued inequalities are obtained automatically, without the need of a Banach- valued theory. This provides a method to prove very fine estimates for a variety of operators which include singular and fractional integrals and their commutators. In particular, we obtain weighted, and vector-valued, extensions of the classical theo- rems of Boyd and Lorentz-Shimogaki. The key is to develop appropriate versions of Rubio de Francia's algorithm.

/pdf/advances-in-mathematics-203-2006-256-318-extrapolation-with-39w7q8zq1s.pdf

Advances in Mathematics, 203 (2006) 256-318. EXTRAPOLATION WITH WEIGHTS, REARRANGEMENT INVARIANT FUNCTION SPACES, MODULAR INEQUALITIES AND APPLICATIONS TO SINGULAR INTEGRALS

The problem of finding optimal lattice domains for kernel operators with values in rearrangement invariant spaces on the interval (0,1) is considered. The techniques used are based on interpolation theory and integration with respect to C((0,1))-valued measures.

/pdf/optimal-domains-for-kernel-operators-via-interpolation-1izrrvfgfk.pdf

Optimal Domains for Kernel Operators via Interpolation

https://euler.us.es/~curbera/publications/IndagMath-17.pdf

Guillermo P. Curbera

Papers

Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals

Operators into L1 of a vector measure and applications to Banach lattices.

Advances in Mathematics, 203 (2006) 256-318. EXTRAPOLATION WITH WEIGHTS, REARRANGEMENT INVARIANT FUNCTION SPACES, MODULAR INEQUALITIES AND APPLICATIONS TO SINGULAR INTEGRALS

Optimal Domains for Kernel Operators via Interpolation

Banach lattices with the Fatou property and optimal domains of kernel operators