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Displaying similar documents to “On maximal functions with rough kernels in L (log L)1/2(Sn-1).”

Rough Marcinkiewicz integral operators on product spaces.

Hussein M. Al-Qassem (2005)

Collectanea Mathematica

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In this paper, we study the Marcinkiewicz integral operators M on the product space R x R. We prove that M is bounded on L(R x R) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space B (S x S) for some q > 1. We also establish the optimality of our condition in the sense that the space B (S x S) cannot be replaced by B (S x S) for any −1 < r < 0. Our results...

Singular integrals and the Newton diagram.

Anthony Carbery, Stephen Wainger, James Wright (2006)

Collectanea Mathematica

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We examine several scalar oscillatory singular integrals involving a real-analytic phase function φ(s,t) of two real variables and illustrate how one can use the Newton diagram of φ to efficiently analyse these objects. We use these results to bound certain singular integral operators.

Perturbations of the H-calculus

N.J. Kalton (2007)

Collectanea Mathematica

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Suppose A is a sectorial operator on a Banach space X, which admits an H-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ S(T)/n <∞ where (S(T))∞ are the singular values of T....

On the Moser-Onofri and Prékopa-Leindler inequalities.

Alessandro Ghigi (2005)

Collectanea Mathematica

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Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that 1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0 for any funcion φ ∈ C∞(S2).

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.

Generalized Lions-Peetre methods of constants and means and operator ideals.

Antonio Manzano, Mieczyslaw Mastylo (2007)

Collectanea Mathematica

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We establish results on interpolation of Rosenthal operators, Banach-Saks operators, Asplund operators and weakly compact operators by means of generalized Lions-Peetre methods of constants and means. Applications are presented for the K-method space generated by the Calderón-Lozanovskii space parameters.