Displaying similar documents to “The exact value of Jung constants in a class of Orlicz function spaces.”

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.

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...

ACM bundles on general hypersurfaces in P of low degree.

Luca Chiantini, Carlo K. Madonna (2005)

Collectanea Mathematica

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In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P a rank 2 vector bundle ε splits if and only if hε(n) = hε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].

Painlevé's problem and analytic capacity.

Xavier Tolsa (2006)

Collectanea Mathematica

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In this paper we survey some recent results in connection with the so called Painlevé's problem and the semiadditivity of analytic capacity γ. In particular, we give the detailed proof of the semiadditivity of the capacity γ, and we show almost completely all the arguments for the proof of the comparability between γ and γ.

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....