Browsing by Subject "Besov"
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Item Open Access Analytic properties of Besov spaces via Bergman projections(American Mathematical Society, 2008) Kaptanoğlu, H. T.; Üreyen, A. E.We consider two-parameter Besov spaces of holomorphic functions on the unit ball of CN: We obtain various exclusions between Besov spaces of di®erent parameters using gap series. We estimate the growth near the boundary and the growth of Taylor coe±cients of functions in these spaces. We ¯nd the unique function with maximum value at each point of the ball in each Besov space. We base our proofs on Bergman projections and imbeddings between Lebesgue classes and Besov spaces. Special cases apply to the Hardy space H2, the Arveson space, the Dirichlet space, and the Bloch space.Item Open Access Carleson measures for Besov spaces on the ball with applications(Academic Press, 2007) Kaptanoǧlu, Hakkı TurgayCarleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are characterized in terms of Berezin transforms and Bergman-metric balls. The measures are defined via natural imbeddings of Besov spaces into Lebesgue classes by certain combinations of radial derivatives. Membership in Schatten classes of the imbeddings is considered too. Some Carleson measures are not finite, but the results extend and provide new insight to those known for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view with the usual Hardy-space Carleson measures is presented by letting the order of the radial derivatives tend to 0. Weak convergence in Besov spaces is also characterized, and weakly 0-convergent families are exhibited. Applications are given to separated sequences, operators of Forelli-Rudin type, gap series, characterizations of weighted Bloch, Lipschitz, and growth spaces, inequalities of Fejér-Riesz and Hardy-Littlewood type, and integration operators of Cesàro type.Item Open Access Precise inclusion relations among Bergman-Besov and Bloch-Lipschitz spaces and H∞ on the unit ball of CN(Wiley-VCH Verlag, 2018) Kaptanoğlu, Hakkı Turgay; Üreyen, A. E.We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new proofs. More importantly, we construct explicit functions in each space that show our relations are strict and the best possible. Many of our inclusions turn out to be sharper than the Sobolev imbeddings.Item Open Access Reproducing Kernels and Radial Differential Operators for Holomorphic and Harmonic Besov Spaces on Unit Balls: a Unified View(Springer, 2010-07-28) Kaptanoğlu, T.Item Open Access Reproducing kernels of harmonic Besov spaces on the ball(Elsevier, 2009-07) Gergun, S.; Kaptanoglu, H. T.; Ureyen, A. E.Besov spaces of harmonic functions on the unit ball of Rn are defined by requiring sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. To cite this article: S. Gergün et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.Item Open Access Toeplitz operators on arveson and dirichlet spaces(Birkhaeuser Science, 2007) Alpay, D.; Kaptanoǧlu, H. T.We define Toeplitz operators on all Dirichlet spaces on the unit ball of CN and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. © Birkhäuser Verlag Basel/Switzerland 2007.