Smulian-Eberlein Spaces
Snakes and articulated arms in an Hilbert space
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
Snarked sums of Banach spaces.
s-numbers of diagonal operators and Besov embeddings
Sobczyk's theorem and the Bounded Approximation Property
Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.
Sobczyk's theorems from A to B.
Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l∞. Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l∞.
Sobolev and isoperimetric inequalities for degenerate metrics.
Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Sobolev classes of mappings on a Carnot-Carathéodory space: various norms and variational problems.
Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
Sobolev embeddings for variable exponent Riesz potentials on metric spaces.
Sobolev embeddings with variable exponent
Sobolev inequalities in 2-D hyperbolic space: A borderline case.
Sobolev inequalities on sets with irregular boundaries.
Sobolev inequalities with variable exponent attaining the values 1 and n
Sobolev multipliers
Sobolev regularity via the convergence rate of convolutions and Jensen’s inequality
We derive a new criterion for a real-valued function to be in the Sobolev space . This criterion consists of comparing the value of a functional with the values of the same functional applied to convolutions of with a Dirac sequence. The difference of these values converges to zero as the convolutions approach , and we prove that the rate of convergence to zero is connected to regularity: if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization...
Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators
Let be a Riemannian manifold, which possesses a transitive Lie group of isometries. We suppose that , and therefore , are compact and connected. We characterize the Sobolev spaces
Sobolev spaces on multiple cones
The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from . The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.
Sobolev theory for non commutative tori