Some classical operators on Lorentz space.
C.J. NEUGEBAUER (1992)
Forum mathematicum
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C.J. NEUGEBAUER (1992)
Forum mathematicum
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Javier Duoandikoetxea (2002)
Publicacions Matemàtiques
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We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered. [Proceedings of the 6th International Conference...
Alberto Criado, Fernando Soria (2016)
Studia Mathematica
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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...
Dmitry V. Rutsky (2014)
Studia Mathematica
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The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded...
Stefano Meda (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Robert Fefferman (1986)
Revista Matemática Iberoamericana
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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].
Mohamed Ali Mourou (2015)
Commentationes Mathematicae Universitatis Carolinae
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This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.
Soulaymane Korry (2002)
Revista Matemática Complutense
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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).
Kislyakov, S.V., Parilov, D.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Parilov, D.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Liu, Lanzhe (2003)
Lobachevskii Journal of Mathematics
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Eugenio Hernández (1989)
Studia Mathematica
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Javier Duoandikoetxea (1991)
Publicacions Matemàtiques
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The aim of this paper is to review a set of articles ([6], [10], [11], [13], [16], [25]) of which José Luis Rubio de Francia was author and co-author written between 1985 and 1987.