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2006•Journal of MathematicsRequires access

LOGARITHMIC CARLESON MEASURES ON THE UNIT BALL

XU Hui-ming

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Abstract

In this paper,we investigate the logarithmic Carleson measures on the unit ball,and characterize the bounded and vanishing logarithmic Carleson measures in terms of Bloch functions.We obtain the analogous result on Bloch space to the Carleson theorem on the Hardy spaces and Bergman spaces. As an application,we give the equivalent condition of boundedness and compactness of the extended Cesaro operator on the Bloch space.

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In this paper,we investigate the logarithmic Carleson measures on the unit ball,and characterize the bounded and vanishing logarithmic Carleson measures in terms of Bloch functions.We obtain the analogous result on Bloch space to the Carleson theorem on the Hardy spaces and Bergman spaces. As an application,we give the equivalent condition of boundedness and compactness of the extended Cesaro operator on the Bloch space.

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Available abstract

In this paper,we investigate the logarithmic Carleson measures on the unit ball,and characterize the bounded and vanishing logarithmic Carleson measures in terms of Bloch functions.We obtain the analogous result on Bloch space to the Carleson theorem on the Hardy spaces and Bergman spaces. As an application,we give the equivalent condition of boundedness and compactness of the extended Cesaro operator on the Bloch space.

Key concepts: Mathematics, Unit sphere, Bloch space, Compact space, Logarithm, Ball (mathematics), Bounded function, Pure mathematics

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