Density results for Sobolev, Besov and Triebel–Lizorkin spaces on rough sets

Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains

Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type ∆u − N(x, u) = F (x), equipped with Dirichlet and Neumann boundary conditions.

Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev Spaces on Complex Balls

on the associated Bergman tree Tn. Combined with recent results about interpolating sequences this leads, for this range of σ, to a characterization of universal interpolating sequences for B 2 and also for its multiplier algebra. However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury-Arveson Hardy space H n = B 1/2 2 . We show that μ is a Carleson mea...

Some results on functionally convex sets in real Banach spaces

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

On Removable Sets for Sobolev Spaces in the Plane

New results on multiplication in Sobolev spaces

We consider the Sobolev (Bessel potential) spaces Hl(R,C), and their standard norms ‖ ‖l (with l integer or noninteger). We are interested in the unknown sharp constant Klmnd in the inequality ‖fg‖l 6 Klmnd‖f‖m‖g‖n (f ∈ Hm(R,C), g ∈ Hn(R,C); 0 6 l 6 m 6 n, m + n − l > d/2); we derive upper and lower bounds K lmnd for this constant. As examples, we give a table of these bounds for d = 1, d = 3 a...