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The characterization of the Carleson measures for analytic Besov spaces: a simple proof  [PDF]
N. Arcozzi,R. Rochberg,E. Sawyer
Mathematics , 2007,
Abstract: We give a simple proof of the characterization of the Carleson measures for the weighted analytic Besov spaces. Such characterization provides some information on the radial variation of an analytic Besov function.
Carleson measures for Besov-Sobolev spaces with applications in the unit ball of $C^n$  [PDF]
Ru Peng,Caiheng Ouyang
Mathematics , 2011,
Abstract: This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces $B_p^\sigma (B)$ and $p$-Carleson measure in the unit ball of ${\bf C}^n$. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on $B_p^\sigma (B)$ spaces by means of Carleson measures for $B_p^\sigma (B)$.
Carleson measures for weighted holomorphic Besov spaces in $\C^n$  [PDF]
Carme Cascante,Joaquin M. Ortega
Mathematics , 2007,
Abstract: We obtain characterizations of positive Borel measures $\mu$ on $\B^n$ so that some weighted holomorphic Besov spaces $B_s^p(w)$ are imbedded in $L^p(d\mu)$, where $w$ is a $B_p$ weight in the unit ball of $\C^n$.
Relations among Besov-Type Spaces, Triebel-Lizorkin-Type Spaces and Generalized Carleson Measure Spaces  [PDF]
Dachun Yang,Wen Yuan
Mathematics , 2011,
Abstract: In this paper, the authors construct some counterexamples to show that the generalized Carleson measure space and the Triebel-Lizorkin-type space are not equivalent for certain parameters, which was claimed to be true in [Taiwanese J. Math. 15 (2011), 919-926]. Moreover, the authors show that for some special parameters, the generalized Carleson measure space, the Triebel-Lizorkin-type space and the Besov-type space coincide with certain Triebel-Lizorkin space, which answers a question posed in Remark 6.11(i) of [Lecture Notes in Mathematics 2005, Springer-Verlag, Berlin, 2010, xi+281 pp.].
Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex Ball  [PDF]
Alexander Volberg,Brett D. Wick
Mathematics , 2009,
Abstract: The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^\sigma_2$ on the complex ball of $\mathbb{C}^d$. In particular, we demonstrate that for any $\sigma> 0$, the Carleson measures for the space are characterized by a "T1 Condition". The method of proof of these results is an extension and another application of the work originated by Nazarov, Treil and the first author.
Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls  [PDF]
N. Arcozzi,R. Rochberg,E. Sawyer
Mathematics , 2007,
Abstract: We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy space.
Generalized Carleson Measure Spaces and Their Applications
Chin-Cheng Lin,Kunchuan Wang
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/879073
Abstract: We introduce the generalized Carleson measure spaces CMO, that extend BMO. Using Frazier and Jawerth's -transform and sequence spaces, we show that, for ∈? and 0<≤1, the duals of homogeneous Triebel-Lizorkin spaces ?, for 1<<∞ and 0<≤1 are CMO?,(/)?(/) and CMO?
Generalized weighted Besov spaces on the Bessel hypergroup  [PDF]
Miloud Assal,Hacen Ben Abdallah
Journal of Function Spaces and Applications , 2006, DOI: 10.1155/2006/587016
Abstract: In this paper we study generalized weighted Besov type spaces on the Bessel-Kingman hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces.
Lp theory for outer measures and two themes of Lennart Carleson united  [PDF]
Yen Do,Christoph Thiele
Mathematics , 2013,
Abstract: We develop a theory of Lp spaces based on outer measures rather than measures. This theory includes the classical Lp theory on measure spaces as special case. It also covers parts of potential theory and Carleson embedding theorems. The theory turns out to be an elegant language to describe aspects of classical singular integral theory such as paraproduct estimates and T(1) theorems, and it is particularly useful for generalizations of singular integral theory in time-frequency analysis. We formulate and prove a generalized Carleson embedding theorem and give a relatively short reduction of basic estimates for the bilinear Hilbert transform to this new Carleson embedding theorem.
Bilinear forms on weighted Besov spaces  [PDF]
Carme Cascante,Joan Fàbrega
Mathematics , 2013,
Abstract: We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers defined in terms of Carleson measures.
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