Displaying similar documents to “A multiplier characterization of analytic UMD spaces”

On a weak type (1,1) inequality for a maximal conjugate function

Nakhlé Asmar, Stephen Montgomery-Smith (1997)

Studia Mathematica

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In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of H p spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.

Martingale operators and Hardy spaces generated by them

Ferenc Weisz (1995)

Studia Mathematica

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Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space H p T is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the B M O q spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the L p norm of the sharp operator is equivalent to the H p T norm. The interpolation spaces between the Hardy and BMO spaces are identified by...

Conjugate martingale transforms

Ferenc Weisz (1992)

Studia Mathematica

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Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

Plurisubharmonic martingales and barriers in complex quasi-Banach spaces

Nassif Ghoussoub, Bernard Maurey (1989)

Annales de l'institut Fourier

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We describe the geometrical structure on a complex quasi-Banach space X that is necessay and sufficient for the existence of boundary limits for bounded, X -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of the unit ball...

Abel means of operator-valued processes

G. Blower (1995)

Studia Mathematica

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Let ( X j ) be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of X n . . . X 2 X 1 to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.