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Displaying similar documents to “Some remarks on Prandtl system”

Averaging theorems for linear operators in compact groups and semigroups

G. Murphy, T. West (1997)

Studia Mathematica

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The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: n - 1 k = 1 n T k P ( n ) where P is a projection associated with the eigenvalue one of T.

On Gateaux differentiable bump functions

Francisco Hernández, Stanimir Troyanski (1996)

Studia Mathematica

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It is shown that the order of Gateaux smoothness of bump functions on a wide class of Banach spaces with unconditional basis is not better than that of Fréchet differentiability. It is proved as well that in the separable case this order for Banach lattices satisfying a lower p-estimate for 1≤ p < 2 can be only slightly better.

On the representation of uncountable symmetric basic sets and its applications

Francisco Hernandez, Stanimir Troyanski (1993)

Studia Mathematica

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It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.

Some integral and maximal operators related to starlike sets

Sagun Chanillo, David Watson, Richard Wheeden (1993)

Studia Mathematica

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We prove two-weight norm estimates for fractional integrals and fractional maximal functions associated with starlike sets in Euclidean space. This is seen to include general positive homogeneous fractional integrals and fractional integrals on product spaces. We consider both weak type and strong type results, and we show that the conditions imposed on the weight functions are fairly sharp.