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Register a new userCarleson embeddings with loss for Bergman-Orlicz spaces of the unit ball
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Authors
Benoit F. Sehba
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We prove Carleson embeddings for Bergman-Orlicz spaces of the unit ball that extend the lower triangle estimates for the usual Bergman spaces.
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In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these spaces.
We prove Carleson embeddings for Bergman spaces of tube domains over symmetric cones, we apply them to characterize symbols of bounded Ces`aro-type operators from weighted Bergman spaces to weighted Besov spaces. We also obtain Schatten class criteria of Toeplitz operators and Ces`aro-type operators on weighted Hilbert-Bergman spaces.
For $mathbb B^n$ the unit ball of $mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Phi_alpha(mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman-Orlicz space $mathcal A^Phi_alpha (mathbb B^n)$ where $Phi$ is either convex or concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman-Orlicz space and also weak factorization theorems involving two Bergman-Orlicz spaces.
For $mathbb B^n$ the unit ball of $mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Phi_alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_alpha^{Phi_1}(mathbb B^n)$ and $A_alpha^{Phi_2}(mathbb B^n)$ where $Phi_1$ and $Phi_2$ are either convex or concave growth functions.
We give in this paper some equivalent definitions of the so called $rho$-Carleson measures when $rho(t)=(log(4/t))^p(loglog(e^4/t))^q$, $0le p,q<infty$. As applications, we characterize the pointwise multipliers on $LMOA(mathbb S^n)$ and from this space to $BMOA(mathbb S^n)$. Boundedness of the Ces`aro type integral operators on $LMOA(mathbb S^n)$ and from $LMOA(mathbb S^n)$ to $BMOA(mathbb S^n)$ is considered as well.
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