Singular integrals on the complex affine group
Garth Gaudry, Peter Sjögren (1998)
Colloquium Mathematicae
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Garth Gaudry, Peter Sjögren (1998)
Colloquium Mathematicae
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Loukas Grafakos, Rodolfo H. Torres (2002)
Publicacions Matemàtiques
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A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....
A. ter Elst, Derek Robinson, Adam Sikora (1998)
Colloquium Mathematicae
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We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian...
Jeff E. Lewis, Cesare Parenti (1980)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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E. Brian Davies (1995)
Journées équations aux dérivées partielles
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Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro (2013)
Studia Mathematica
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In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón-Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.
José María Martell (2004)
Studia Mathematica
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In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates...
Atanas Stefanov (2001)
Studia Mathematica
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We prove weak type (1,1) estimates for a special class of Calderón-Zygmund homogeneous kernels represented as l¹ sums of "equidistributed" H¹ atoms on 𝕊¹.
Josefina Alvarez, Mario Milman (1986)
Revista Matemática Iberoamericana
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In this article we consider a theory of vector valued strongly singular operators. Our results include Lp, Hp and BMO continuity results. Moreover, as is well known, vector valued estimates are closely related to weighted norm inequalities. These results are developed in the first four sections of our paper. In section 5 we use our vector valued singular integrals to estimate the corresponding maximal operators. Finally in section 6 we discuss...
Richard Beals (1979)
Annales de l'institut Fourier
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Continuity in spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.