Fractional integration on the space and its dual
Fractional Maximal Functions in Metric Measure Spaces
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Fractional power function spaces associated to regular Sturm--Liouville problems.
Fractional powers of operators and Bessel potentials on Hilbert space
Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
We study the notion of fractional -differentiability of order along vector fields satisfying the Hörmander condition on . We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different -norms are equivalent. We also prove a local embedding , where q is a suitable exponent greater than p.
Frame characterizations of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type and their applications.
Frames associated with expansive matrix dilations.
We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.
Fuglede's theorem in variable exponent Sobolev space.
Function algebras of Besov and Triebel-Lizorkin-type
We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
Function spaces and spectra of elliptic operators on a class of hyperbolic manifolds
The paper deals with quarkonial decompositions and entropy numbers in weighted function spaces on hyperbolic manifolds. We use these results to develop a spectral theory of related Schrödinger operators in these hyperbolic worlds.
Function spaces have essential sets
It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.
Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
Function spaces of type Bspq and Fspq cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on Rn and in smooth bounded domains in Rn including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a...
Function spaces of generalised smoothness [Book]
Function spaces of Nikolskii type on compact manifold
Nikolskii spaces were defined by way of translations on and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in , we get an equivalent definition if we replace translations by all isometries of . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...
Function Spaces of Sobolev Type on Riemannian Symmetric Manifolds.
Function spaces on the snowflake
We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces [Book]
Function spaces with dominating mixed smoothness [Book]
Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains
We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.
Functions with prescribed singularities
The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the map we construct...