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Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents

Hongbin Wang, Chenchen Niu (2024)

Czechoslovak Mathematical Journal

We introduce a type of n -dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.

Bilinear multipliers on Lorentz spaces

Francisco Villarroya (2008)

Czechoslovak Mathematical Journal

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

Bilinear operators associated with Schrödinger operators

Chin-Cheng Lin, Ying-Chieh Lin, Heping Liu, Yu Liu (2011)

Studia Mathematica

Let L = -Δ + V be a Schrödinger operator in d and H ¹ L ( d ) be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by T ± ( f , g ) ( x ) = ( T f ) ( x ) ( T g ) ( x ) ± ( T f ) ( x ) ( T g ) ( x ) , where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from L p ( d ) × L q ( d ) to H ¹ L ( d ) for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.

BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.

Joan Mateu, Joan Verdera Melenchón (1988)

Revista Matemática Iberoamericana

The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...

Boundedness and compactness of some operators on discrete Morrey spaces

Martha Guzmán-Partida (2021)

Commentationes Mathematicae Universitatis Carolinae

We consider discrete versions of Morrey spaces introduced by Gunawan et al. in papers published in 2018 and 2019. We prove continuity and compactness of multiplication operators and commutators acting on them.

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