Matrix spaces and Schur multipliers : matriceal harmonic analysis / Lars-Erik Persson and Nicolae Popa.

Includes bibliographical references (pages 185-189) and index.

1. Introduction.
1.1. Preliminary notions and notations --
2. Integral operators in infinite matrix theory.
2.1. Periodical integral operators.
2.2. Nonperiodical integral operators.
2.3. Some applications of integral operators in the classical theory of infinite matrices --
3. Matrix versions of spaces of periodical functions.
3.1. Preliminaries.
3.2. Some properties of the space C[symbol].
3.3. Another characterization of the space C[symbol] and related results.
3.4. A matrix version for functions of bounded variation.
3.5. Approximation of infinite matrices by matriceal Haar polynomials.
3.6. Lipschitz spaces of matrices; a characterization --
4. Matrix versions of Hardy spaces.
4.1. First properties of matriceal Hardy space.
4.2. Hardy-Schatten spaces.
4.3. An analogue of the Hardy inequality in T[symbol].
4.4. The Hardy inequality for matrix-valued analytic functions. 4.5. A characterization of the space T[symbol].
4.6. An extension of Shields's inequality --
5. The matrix version of BMOA.
5.1. First properties of BMOA[symbol] space.
5.2. Another matrix version of BMO and matriceal Hankel operators.
5.3. Nuclear Hankel operators and the space M[symbol] --
6. Matrix version of Bergman spaces.
6.1. Schatten class version of Bergman spaces.
6.2. Some inequalities in Bergman-Schatten classes.
6.3. A characterization of the Bergman-Schatten space.
6.4. Usual multipliers in Bergman-Schatten spaces --
7. A matrix version of Bloch spaces.
7.1. Elementary properties of Bloch matrices.
7.2. Matrix version of little Bloch space --
8. Schur multipliers on analytic matrix spaces--

Bibliography--
Index--

This book gives a unified approach to the theory concerning a new matrix version of classical harmonic analysis. Most results in the book have their analogues as classical or newer results in harmonic analysis. It can be used as a source for further research in many areas related to infinite matrices. In particular, it could be a perfect starting point for students looking for new directions to write their PhD thesis as well as for experienced researchers in analysis looking for new problems with great potential to be very useful both in pure and applied mathematics where classical analysis has been used, for example, in signal processing and image analysis.