Sobolev Constants in Disconnected Domains

2006 ◽  
Author(s):  
Catherine Bandle
Keyword(s):  
Sobolev Constants ◽  
Disconnected Domains

Bergman Spaces on Disconnected Domains

1996 ◽  
Vol 48 (2) ◽  
pp. 225-243
Author(s):  
Alexandru Aleman ◽  
Stefan Richter ◽  
William T. Ross
Keyword(s):  
Measure Zero ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Invariant Subspaces ◽  
Compact Set ◽  
Bounded Region ◽  
Area Measure ◽  
Weak Star ◽  
Harmonic Dirichlet Space ◽  
Disconnected Domains

AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.

scholarly journals Sobolev inequalities for fractional Neumann Laplacians on half spaces

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Roberta Musina ◽  
Alexander I. Nazarov
Keyword(s):  
Half Space ◽  
Sobolev Inequalities ◽  
Neumann Laplacian ◽  
Sobolev Constants

Abstract We consider different fractional Neumann Laplacians of order {s\in(0,1)} on domains {\Omega\subset\mathbb{R}^{n}} , namely, the restricted Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{R}}}} , the semirestricted Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{Sr}}}} and the spectral Neumann Laplacian {{(-\Delta_{\Omega}^{N})^{s}_{\mathrm{Sp}}}} . In particular, we are interested in the attainability of Sobolev constants for these operators when Ω is a half-space.

scholarly journals Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains

2004 ◽  
Vol 14 (4) ◽  
pp. 1741-1765 ◽  
Author(s):  
Mark Jerrum ◽  
Jung-Bae Son ◽  
Prasad Tetali ◽  
Eric Vigoda
Keyword(s):  
Markov Chains ◽  
Sobolev Constants

Optimal bounds for bifurcation values of a superlinear periodic problem

2005 ◽  
Vol 135 (1) ◽  
pp. 119-132 ◽  
Author(s):  
Rafael Ortega ◽  
Meirong Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Periodic Problem ◽  
Optimal Bounds ◽  
Sobolev Constants ◽  
Dynamic Bifurcation

In this paper we will show that the optimal bounds for certain static and dynamic bifurcation values of periodic solutions of some superlinear differential equations can be expressed explicitly using Sobolev constants.

Estimates for the Torsion Function and Sobolev Constants

2011 ◽  
Vol 36 (4) ◽  
pp. 607-616 ◽  
Author(s):  
Michiel van den Berg
Keyword(s):  
Torsion Function ◽  
Sobolev Constants
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