Vladimir Maz’ya, Gershon Kresin (auth.)9783540695738, 3-540-69573-7
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.
Table of contents :
Front Matter….Pages I-XV
Estimates for analytic functions bounded with respect to their real part….Pages 1-16
Estimates for analytic functions with respect to the Lp-norm of RΔf on the circle….Pages 17-35
Estimates for analytic functions by the best L p -approximation of Rf on the circle….Pages 37-55
Estimates for directional derivatives of harmonic functions….Pages 57-67
Estimates for derivatives of analytic functions….Pages 69-98
Bohr’s type real part estimates….Pages 99-114
Estimates for the increment of derivatives of analytic functions….Pages 115-128
Back Matter….Pages 129-144
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