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Compact differences of composition operators on weighted Dirichlet spaces

Robert Allen, Katherine Heller, Matthew Pons (2014)

Open Mathematics

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

Compact embedding theorems for generalized Sobolev spaces

Maria Manfredini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we give some compact embedding theorems for Sobolev spaces, related to m -tuples of vectors fields of C 1 class on R N .

Compact embeddings of Brézis-Wainger type.

Fernando Cobos, Thomas Kühn, Tomas Schonbek (2006)

Revista Matemática Iberoamericana

Let Ω be a bounded domain in Rn and denote by idΩ the restriction operator from the Besov space Bpq1+n/p(Rn) into the generalized Lipschitz space Lip(1,-α)(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idΩ) ~ k-1/p if α > max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.

Compact endomorphisms of H ( D )

Joel Feinstein, Herbert Kamowitz (1999)

Studia Mathematica

Compact composition operators on H ( G ) , where G is a region in the complex plane, and the spectra of these operators were described by D. Swanton ( Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on H ( D ) , where D is the unit disc, and determine their spectra.

Compact operators and approximation spaces

Fernando Cobos, Oscar Domínguez, Antón Martínez (2014)

Colloquium Mathematicae

We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.

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