scholarly journals Double integral characterizations of harmonic Bergman spaces

2011 ◽  
Vol 379 (2) ◽  
pp. 889-909 ◽  
Author(s):  
Boo Rim Choe ◽  
Kyesook Nam
Keyword(s):  
Bergman Spaces ◽  
Double Integral ◽  
Harmonic Bergman Spaces

scholarly journals Compact Toeplitz operators on weighted harmonic Bergman spaces

1998 ◽  
Vol 64 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Harmonic Bergman Spaces

AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

scholarly journals Harmonic Bergman spaces on the complement of a lattice

Filomat ◽  
2013 ◽  
Vol 27 (2) ◽  
pp. 245-249
Author(s):  
Abejela Shkheam ◽  
Ali Abaob ◽  
Milos Arsenovic
Keyword(s):  
Bergman Spaces ◽  
Harmonic Bergman Spaces

scholarly journals Harmonic Besov spaces on the ball

2016 ◽  
Vol 27 (09) ◽  
pp. 1650070 ◽  
Author(s):  
Seçil Gergün ◽  
H. Turgay Kaptanoğlu ◽  
A. Ersin Üreyen
Keyword(s):  
Besov Spaces ◽  
Bergman Spaces ◽  
Reproducing Kernels ◽  
Integral Representations ◽  
Kernel Estimates ◽  
Harmonic Bergman Spaces ◽  
Infinite Sums ◽  
Bergman Projections ◽  
Derivatives Of

We initiate a detailed study of two-parameter Besov spaces on the unit ball of [Formula: see text] consisting of harmonic functions whose sufficiently high-order radial derivatives lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels are weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. Estimates of the growth of kernels lead to characterization of integral transformations on Lebesgue classes. The transformations allow us to conclude that the order of the radial derivative is not a characteristic of a Besov space as long as it is above a certain threshold. Using kernels, we define generalized Bergman projections and characterize those that are bounded from Lebesgue classes onto Besov spaces. The projections provide integral representations for the functions in these spaces and also lead to characterizations of the functions in the spaces using partial derivatives. Several other applications follow from the integral representations such as atomic decomposition, growth at the boundary and of Fourier coefficients, inclusions among them, duality and interpolation relations, and a solution to the Gleason problem.

scholarly journals AN INEQUALITY RELATED TO THE GEHRING–HALLENBECK THEOREM ON RADIAL LIMITS OF FUNCTIONS IN THE HARMONIC BERGMAN SPACES

2008 ◽  
Vol 50 (3) ◽  
pp. 433-435 ◽  
Author(s):  
MIROSLAV PAVLOVIĆ
Keyword(s):  
Unit Disk ◽  
Bergman Spaces ◽  
Radial Limits ◽  
Harmonic Bergman Spaces ◽  
Image Position

AbstractFor a function u harmonic in the unit disk , there holds the inequality where p > 0 and β > −1, and .

Harmonic Bergman Spaces

2001 ◽  
pp. 171-190
Author(s):  
Sheldon Axler ◽  
Paul Bourdon ◽  
Wade Ramey
Keyword(s):  
Bergman Spaces ◽  
Harmonic Bergman Spaces
Sign in / Sign up

Export Citation Format

Share Document