An ill-posed nonlocal two-point problem for systems of partial differential equations.
An imbedding theorem for H°(G,Ω)-spaces
An indecomposable Banach space of continuous functions which has small density
Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.
An inequality for the indefinite integral of a function in
An inequality in Orlicz function spaces with Orlicz norm
We use Simonenko quantitative indices of an -function to estimate two parameters and in Orlicz function spaces with Orlicz norm, and get the following inequality: , where and are Simonenko indices. A similar inequality is obtained in with Orlicz norm.
An integral extrapolation theorem with applcations
An interpolation inequality in exterior domains
An interpolation inequality involving Hölder norms.
An interpolation theorem with -weighted spaces
An interpolatory estimate for the UMD-valued directional Haar projection [Book]
An invariant subspace of the Bergman space having the codimension two property.
An isomorphic Banach-Stone theorem
An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces
An -criterion of amenability for a locally compact group.
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.
An L...-Estimate for the gradient of extremals.
An -functional calculus for power-bounded operators on certain UMD spaces
For 1 ≤ q < ∞, let denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction q >...
An operator characterization of -spaces in a class of Orlicz spaces
We consider an embedding of the group of invertible transformations of [0,1] into the algebra of bounded linear operators on an Orlicz space. We show that if this embedding preserves the group action then the Orlicz space is an -space for some 1 ≤ p < ∞.
An optimal endpoint trace embedding
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
An optimal symbolic calculus on Besov algebras