scholarly journals Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball

2008 ◽  
Vol 136 (07) ◽  
pp. 2483-2492 ◽  
Author(s):  
Renata Otáhalová
Keyword(s):  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Reproducing Kernels ◽  
The Real ◽  
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 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 Toeplitz operators on harmonic Bergman spaces

2004 ◽  
Vol 174 ◽  
pp. 165-186 ◽  
Author(s):  
Boo Rim Choe ◽  
Young Joo Lee ◽  
Kyunguk Na
Keyword(s):  
Toeplitz Operators ◽  
Bergman Spaces ◽  
The Other ◽  
Essential Spectra ◽  
Schatten Classes ◽  
Harmonic Bergman Spaces ◽  
Bounded Smooth ◽  
Uniformly Continuous

AbstractWe study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.

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