Sharp Real-Part Theorems
Maz'ya, Vladimir.
Sharp Real-Part Theorems A Unified Approach / [electronic resource] : by Vladimir Maz'ya, Gershon Kresin. - XV, 145 p. online resource. - Lecture Notes in Mathematics, 1903 0075-8434 ; . - Lecture Notes in Mathematics, 1903 .
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.
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.
9783540695745
10.1007/3-540-69573-7 doi
Functions of complex variables.
Potential theory (Mathematics).
Functions of a Complex Variable.
Potential Theory.
QA331-355
515.9
Sharp Real-Part Theorems A Unified Approach / [electronic resource] : by Vladimir Maz'ya, Gershon Kresin. - XV, 145 p. online resource. - Lecture Notes in Mathematics, 1903 0075-8434 ; . - Lecture Notes in Mathematics, 1903 .
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.
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.
9783540695745
10.1007/3-540-69573-7 doi
Functions of complex variables.
Potential theory (Mathematics).
Functions of a Complex Variable.
Potential Theory.
QA331-355
515.9