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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 Besov spaces involving only slowly varying smoothness

António Caetano, Amiran Gogatishvili, Bohumír Opic (2011)

Czechoslovak Mathematical Journal

We characterize compact embeddings of Besov spaces B p , r 0 , b ( ℝ n ) involving the zero classical smoothness and a slowly varying smoothness b into Lorentz-Karamata spaces L p , q ; b ¯ ( Ω ) , where Ω is a bounded domain in ℝ n and b ¯ is another slowly varying function.

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 homomorphisms between algebras of analytic functions

Richard Aron, Pablo Galindo, Mikael Lindström (1997)

Studia Mathematica

We prove that every weakly compact multiplicative linear continuous map from H ∞ ( D ) into H ∞ ( D ) is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra H ∞ ( B E ) , where B E is the open unit ball of an infinite-dimensional Banach space E.

Currently displaying 361 – 380 of 881