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Extensions of weak type multipliers

P. Mohanty, S. Madan (2003)

Studia Mathematica

We prove that if Λ M p ( N ) and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where M p ( N ) is the space of multipliers of L p ( N ) .

Extensions uniformes des formes linéaires positives

Hicham Fakhoury (1973)

Annales de l'institut Fourier

Soit M un sous-espace fermé d’un espace de Banach ordonné V  ; ce travail propose des conditions nécessaires et suffisantes pour qu’il existe a 1 , tel que toute forme linéaire f positive et continue sur M admette une extension linéaire f ˜ positive et continue sur V , vérifiant f ˜ a f . On termine par l’exemple d’un couple ( M , V ) ne possédant pas la propriété précédente bien que toute forme linéaire positive continue sur M se prolonge en une forme linéaire du même type en V .

External approximation of first order variational problems via W-1,p estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving W - 1 , p norms obtained by Nečas and on the general framework of Γ-convergence theory.

Extrapolation of Sobolev imbeddings.

M. Krbec (1997)

Collectanea Mathematica

We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.

Extrapolation theory for the real interpolation method.

María J. Carro, Joaquim Martín (2002)

Collectanea Mathematica

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega.

Extremal functions of the Nevanlinna-Pick problem and Douglas algebras

V. Tolokonnikov (1993)

Studia Mathematica

The Nevanlinna-Pick problem at the zeros of a Blaschke product B having a solution of norm smaller than one is studied. All its extremal solutions are invertible in the Douglas algebra D generated by B. If B is a finite product of sparse Blaschke products (Newman Blaschke products, Frostman Blaschke products) then so are all the extremal solutions. For a Blaschke product B a formula is given for the number C(B) such that if the NP-problem has a solution of norm smaller than C(B) then all its extremal...

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