Displaying similar documents to “Rough singular integral operators with Hardy space function kernels on a product domain”

Some new Hardy spaces L ² H R q ( ² + × ² + ) (0 < q ≤ 1)

Dachun Yang (1994)

Studia Mathematica

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For 0 < q ≤ 1, the author introduces a new Hardy space L ² H q ( ² + × ² + ) on the product domain, and gives its generalized Lusin-area characterization. From this characterization, a φ-transform characterization in M. Frazier and B. Jawerth’s sense is deduced.

Two-parameter Hardy-Littlewood inequalities

Ferenc Weisz (1996)

Studia Mathematica

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The inequality (*) ( | n | = 1 | m | = 1 | n m | p - 2 | f ̂ ( n , m ) | p ) 1 / p C p ƒ H p (0 < p ≤ 2) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space H p on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in L p whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier...

Multiplier transformations on H p spaces

Daning Chen, Dashan Fan (1998)

Studia Mathematica

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The authors obtain some multiplier theorems on H p spaces analogous to the classical L p multiplier theorems of de Leeuw. The main result is that a multiplier operator ( T f ) ( x ) = λ ( x ) f ̂ ( x ) ( λ C ( n ) ) is bounded on H p ( n ) if and only if the restriction λ ( ε m ) m Λ is an H p ( T n ) bounded multiplier uniformly for ε>0, where Λ is the integer lattice in n .

On Hardy spaces in complex ellipsoids

Thomas Hansson (1999)

Annales de l'institut Fourier

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This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space H 1 . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define H 1 with respect to a certain measure that degenerates near...

A variant sharp estimate for multilinear singular integral operators

Guoen Hu, Dachun Yang (2000)

Studia Mathematica

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We establish a variant sharp estimate for multilinear singular integral operators. As applications, we obtain the weighted norm inequalities on general weights and certain L l o g + L type estimates for these multilinear operators.

L p estimates for Schrödinger operators with certain potentials

Zhongwei Shen (1995)

Annales de l'institut Fourier

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We consider the Schrödinger operators - Δ + V ( x ) in n where the nonnegative potential V ( x ) belongs to the reverse Hölder class B q for some q n / 2 . We obtain the optimal L p estimates for the operators ( - Δ + V ) i γ , 2 ( - Δ + V ) - 1 , ( - Δ + V ) - 1 / 2 and ( - Δ + V ) - 1 where γ . In particular we show that ( - Δ + V ) i γ is a Calderón-Zygmund operator if V B n / 2 and ( - Δ + V ) - 1 / 2 , ( - Δ + V ) - 1 are Calderón-Zygmund operators if V B n .

The local versions of H p ( n ) spaces at the origin

Shan Lu, Da Yang (1995)

Studia Mathematica

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Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces H K ̇ q α , p ( n ) which are the local versions of H p ( n ) spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth’s sense. We also prove an interpolation theorem for operators on H K ̇ q α , p ( n ) and discuss the H K ̇ q α , p ( n ) -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...