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An explicit right inverse of the divergence operator which is continuous in weighted norms

100%

Durán R., Muschietti M.

Studia Mathematica

2001

tom 148

nr 3

207-219

The existence of a continuous right inverse of the divergence operator in $W₀^{1,p}(Ω)ⁿ$, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.

Multipliers of Laplace transform type for Laguerre and Hermite expansions

81%

De Nápoli P., Drelichman I., Durán R.

Studia Mathematica

2011

tom 203

nr 3

265-290

We present a new criterion for the weighted $L^{p}-L^{q}$ boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.

Ograniczanie wyników

2 Studia Mathematica

2 Durán R.

1 De Nápoli P.

1 Drelichman I.

1 Muschietti M.

1 2011

1 2001

Wyniki wyszukiwania

An explicit right inverse of the divergence operator which is continuous in weighted norms

Multipliers of Laplace transform type for Laguerre and Hermite expansions