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Maximal singular integrals on product homogeneous groups

Yong Ding, Shuichi Sato (2014)

Studia Mathematica

We prove L p boundedness for p ∈ (1,∞) of maximal singular integral operators with rough kernels on product homogeneous groups under a sharp integrability condition of the kernels.

Mean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels

Liu Lanzhe (2014)

Archivum Mathematicum

In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are proved. The integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

Medians, continuity, and vanishing oscillation

Jonathan Poelhuis, Alberto Torchinsky (2012)

Studia Mathematica

We consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a cube of ℝⁿ.

Mixed A p - A estimates with one supremum

Andrei K. Lerner, Kabe Moen (2013)

Studia Mathematica

We establish several mixed A p - A bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the A part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily smaller...

Modulation invariant and multilinear singular integral operators

Michael Christ (2005/2006)

Séminaire Bourbaki

In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...

Muckenhoupt-Wheeden conjectures in higher dimensions

Alberto Criado, Fernando Soria (2016)

Studia Mathematica

In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical Calderón-Zygmund...

Multilinear almost diagonal estimates and applications

Árpád Bényi, Nikolaos Tzirakis (2004)

Studia Mathematica

We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.

Multilinear Calderón-Zygmund operators on weighted Hardy spaces

Wenjuan Li, Qingying Xue, Kôzô Yabuta (2010)

Studia Mathematica

Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined A p weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for multilinear...

Multilinear commutators for fractional integrals in non-homogeneous spaces.

Guoen Hu, Yan Meng, Dachung Yang (2004)

Publicacions Matemàtiques

Under the assumption that m is a non-doubling measure on Rd, the authors obtain the (Lp,Lq)-boundedness and the weak type endpoint estimate for the multilinear commutators generated by fractional integrals with RBMO (m) functions of Tolsa or with Osc exp Lr(m) functions for r greater than or equal to 1, where Osc exp Lr(m) is a space of Orlicz type satisfying that Osc exp Lr(m)=RBMO(m) if r=1 and Osc exp Lr(m) is a subset of RBMO(m) if r>1.

Multi-Morrey spaces for non-doubling measures

Suixin He (2019)

Czechoslovak Mathematical Journal

The spaces of multi-Morrey type for positive Radon measures satisfying a growth condition on d are introduced. After defining the spaces, we investigate the multilinear maximal function, the multilinear fractional integral operator and the multilinear Calderón-Zygmund operators, respectively, from multi-Morrey spaces to Morrey spaces.

Multiparameter ergodic Cesàro-α averages

A. L. Bernardis, R. Crescimbeni, C. Ferrari Freire (2015)

Colloquium Mathematicae

Net (X,ℱ,ν) be a σ-finite measure space. Associated with k Lamperti operators on L p ( ν ) , T , . . . , T k , n ̅ = ( n , . . . , n k ) k and α ̅ = ( α , . . . , α k ) with 0 < α j 1 , we define the ergodic Cesàro-α̅ averages n ̅ , α ̅ f = 1 / ( j = 1 k A n j α j ) i k = 0 n k i = 0 n j = 1 k A n j - i j α j - 1 T k i k T i f . For these averages we prove the almost everywhere convergence on X and the convergence in the L p ( ν ) norm, when n , . . . , n k independently, for all f L p ( d ν ) with p > 1/α⁎ where α = m i n 1 j k α j . In the limit case p = 1/α⁎, we prove that the averages n ̅ , α ̅ f converge almost everywhere on X for all f in the Orlicz-Lorentz space Λ ( 1 / α , φ m - 1 ) with φ ( t ) = t ( 1 + l o g t ) m . To obtain the result in the limit case we need to study...

Multiparameter singular integrals and maximal functions

Fulvio Ricci, Elias M. Stein (1992)

Annales de l'institut Fourier

We prove L p -boundedness for a class of singular integral operators and maximal operators associated with a general k -parameter family of dilations on R n . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.

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