Displaying similar documents to “A study on some new types of Hardy-Hilbert's integral inequality.”

Bloch type spaces on the unit ball of a Hilbert space

Zhenghua Xu (2019)

Czechoslovak Mathematical Journal

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We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

A sharp estimate for the Hardy-Littlewood maximal function

Loukas Grafakos, Stephen Montgomery-Smith, Olexei Motrunich (1999)

Studia Mathematica

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The best constant in the usual L p norm inequality for the centered Hardy-Littlewood maximal function on ℝ 1 is obtained for the class of all “peak-shaped” functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.

Hilbert spaces of analytic functions of infinitely many variables

O. V. Lopushansky, A. V. Zagorodnyuk (2003)

Annales Polonici Mathematici

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We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.