Sharp Real-Part Theorems: A Unified Approach

ISBN-13: 9783540695738 / Angielski / Miękka / 2007 / 164 str.

Gershon Kresin; Vladimir G. Maz'ya; T. Shaposhnikova

Opis

This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.

Recenzje

From the reviews:

"The subject matter of the book under review is a unified approach to sharp pointwise estimates for analytic functions ... . An index, a list of symbols and 92 references are also provided. Analysts will find this book as an excellent resource for 'real-part theorems' and related inequalities. One can expect rich opportunities for extending the indicated inequalities to analytic functions of several complex variables and solutions of partial differential equations. This work is a welcome addition to the literature." (George Csordas, Zentralblatt MATH, Vol. 1117 (19), 2007)

Spis treści

Estimates for analytic functions bounded with respect to their real part.- Estimates for analytic functions with respect to the Lp-norm of R?f on the circle.- Estimates for analytic functions by the best Lp-approximation of Rf on the circle.- Estimates for directional derivatives of harmonic functions.- Estimates for derivatives of analytic functions.- Bohr's type real part estimates.- Estimates for the increment of derivatives of analytic functions.

Blurb

This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory. Rich opportunities are anticipated to extend these inequalities to analytic functions of several complex variables and solutions of partial differential equations.