Displaying similar documents to “Boundary values for Sobolev-spaces with weights. Density of D ( Ω ) in W p , γ 0 , ⋯ , γ r s ( Ω ) and in H p , γ 0 , ⋯ , γ r s ( Ω ) for s > 0 and r = s - 1 p - ”

Imbedding theorems of Sobolev spaces into Lorentz spaces

Luc Tartar (1998)

Bollettino dell'Unione Matematica Italiana

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In questo articolo vengono date alcune varianti del teorema di immersione di Sobolev in spazi di Lorentz. In particolare si dimostra un teorema di immersione per spazi di Sobolev anisotropi supponendo che le derivate parziali appartengono a spazi di Lorentz diversi, anche nel caso limite, corrispondente all’estensione di Brezis-Wainger del teorema di Trudinger per W 1 , N ( ℝ N ) .

Notes on interpolation of Hardy spaces

Quanhua Xu (1992)

Annales de l'institut Fourier

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Let H p denote the usual Hardy space of analytic functions on the unit disc ( 0 < p ≤ ∞ ) . We prove that for every function f ∈ H 1 there exists a linear operator T defined on L 1 ( T ) which is simultaneously bounded from L 1 ( T ) to H 1 and from L ∞ ( T ) to H ∞ such that T ( f ) = f . Consequently, we get the following results ( 1 ≤ p 0 , p 1 ≤ ∞ ) : 1) ( H p 0 , H p 1 ) is a Calderon-Mitjagin couple; 2) for any interpolation functor F , we have F ( H p 0 , H p 1 ) = H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) , where H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) denotes the closed subspace of F ( L p 0 ( T ) , L p 1 ( T ) ) of all functions whose Fourier coefficients...