TY - JOUR

T1 - Multidimensional harmonic functions analogues of sharp real-part theorems in complex function theory

AU - Kresin, Gershon

N1 - Publisher Copyright:
© 2009 Birkhäuser Verlag Basel/Switzerland.

PY - 2009

Y1 - 2009

N2 - In the present paper, the sharp multidimensional analogues of Lindelöf inequality and similar estimates for analytic functions are considered. Using a sharp inequality for the gradient of a bounded or semibounded harmonic function in a ball, one arrives at improved estimates (compared with the known ones) for the gradient of harmonic functions in an arbitrary sub-domain of Rn. A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a half-space is obtained under the assumption that function’s boundary values belong to Lp. This representation is realized in the three-dimensional case and the values of sharp constants are explicitly given for p = 1, 2, ∞.

AB - In the present paper, the sharp multidimensional analogues of Lindelöf inequality and similar estimates for analytic functions are considered. Using a sharp inequality for the gradient of a bounded or semibounded harmonic function in a ball, one arrives at improved estimates (compared with the known ones) for the gradient of harmonic functions in an arbitrary sub-domain of Rn. A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a half-space is obtained under the assumption that function’s boundary values belong to Lp. This representation is realized in the three-dimensional case and the values of sharp constants are explicitly given for p = 1, 2, ∞.

KW - Gradient of a harmonic function

KW - Multidimensional analogues of real-part theorems

KW - Sharp parametric pointwise estimates

UR - http://www.scopus.com/inward/record.url?scp=85069523322&partnerID=8YFLogxK

U2 - 10.1007/978-3-7643-9898-9_10

DO - 10.1007/978-3-7643-9898-9_10

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AN - SCOPUS:85069523322

SN - 0255-0156

VL - 193

SP - 115

EP - 128

JO - Operator Theory: Advances and Applications

JF - Operator Theory: Advances and Applications

ER -