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Spaces of analytic functions of HardyBloch type
 J. ANAL. MATH
"... For 0 < p ≤ ∞ and 0 < q ≤ ∞, the space of HardyBloch type B(p, q) consists of those functions f which are analytic in the unit disk D such that (1 − r)Mp(r, f ′) ∈ Lq(dr/(1 − r)). We note that B(∞,∞) coincides with the Bloch space B and that B ⊂ B(p,∞), for all p. Also, the space B(p, p) ..."
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Cited by 13 (5 self)
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For 0 < p ≤ ∞ and 0 < q ≤ ∞, the space of HardyBloch type B(p, q) consists of those functions f which are analytic in the unit disk D such that (1 − r)Mp(r, f ′) ∈ Lq(dr/(1 − r)). We note that B(∞,∞) coincides with the Bloch space B and that B ⊂ B(p,∞), for all p. Also, the space B(p, p) is the Dirichlet space Dpp−1. We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about the mean growth of the B(p, q)functions. In particular, we prove that if f is an analytic function in D and 2 ≤ p < ∞, then the condition Mp(r, f ′) = O (1 − r)−1, as r → 1, implies that Mp(r, f) = O
Carleson measures for spaces of Dirichlet type
"... Dedicated to Albert Baernstein on the occasion of his 65th birthday Abstract. If 0 < p < ∞ and α> −1, the space Dpα consists of those functions f which are analytic in the unit disc D and have the property that f ′ belongs to the weighted Bergman space Apα. In 1999, Z. Wu obtained a charact ..."
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Dedicated to Albert Baernstein on the occasion of his 65th birthday Abstract. If 0 < p < ∞ and α> −1, the space Dpα consists of those functions f which are analytic in the unit disc D and have the property that f ′ belongs to the weighted Bergman space Apα. In 1999, Z. Wu obtained a characterization of the Carleson measures for the spaces Dpα for certain values of p and α. In particular, he proved that, for 0 < p ≤ 2, the Carleson measures for the space Dpp−1 are precisely the classical Carleson measures. Wu also conjectured that this result remains true for 2 < p < ∞. In this paper we prove that this conjecture is false. Indeed, we prove that if 2 < p < ∞, then there exists g analytic in D such that the measure µg,p on D defined by dµg,p(z) = (1−z2)p−1g′(z)p dx dy is not a Carleson measure for Dpp−1 but is a classical Carleson measure. We obtain also some sufficient conditions for multipliers of the spaces Dpp−1.
On Blochtype functions with Hadamard gaps,”
 Abstract and Applied Analysis,
, 2007
"... We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for ,∞ as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given. ..."
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Cited by 4 (1 self)
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We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for ,∞ as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given.
Analytic Properties of Besov Spaces via Bergman Projections
 CONTEMPORARY MATHEMATICS
"... We consider twoparameter Besov spaces of holomorphic functions on the unit ball of CN. We obtain various exclusions between Besov spaces of different parameters using gap series. We estimate the growth near the boundary and the growth of Taylor coefficients of functions in these spaces. We find t ..."
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Cited by 2 (1 self)
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We consider twoparameter Besov spaces of holomorphic functions on the unit ball of CN. We obtain various exclusions between Besov spaces of different parameters using gap series. We estimate the growth near the boundary and the growth of Taylor coefficients of functions in these spaces. We find 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.
On characterizations of Blochtype, Hardytype and Lipschitztype spaces
 Math. Z
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