Displaying similar documents to “The martingale Smirnov class.”

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

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The martingale Hardy space H p ( [ 0 , 1 ) 2 ) and the classical Hardy space H p ( 2 ) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from H p to L p (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified...

Atomic decomposition of a weighted inductive limit.

Jari Taskinen (2003)

RACSAM

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Estudiamos algunas cuestiones estructurales acerca del espacio localmente convexo H , que está formado por funciones analíticas en el disco unidad abierto. Construimos una descomposición atómica de este espacio, usando un retículo de puntos del disco unidad que es más denso que el usual. También demostramos que H no es nuclear.

Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

Manfred Scheve (1991)

Studia Mathematica

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Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from...

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...