We study n-term wavelet-type approximations in Besov and Triebel–Lizorkin spaces. In particular, we characterize spaces of functions which have prescribed degree of n-term approximation in terms of interpolation spaces. These results are applied to identify interpolation spaces between Triebel–Lizorkin and Besov spaces.

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.

In this paper, we consider the compressible Navier–Stokes system around constant equilibrium states and prove existence of a unique global solution for arbitrarily large initial data in scaling critical Besov space provided that Mach number is sufficiently small, incompressible part velocity generates equation. Moreover, low limit show converges to equation some time norms.

We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with energetic variational approach we obtain general system modeling evolution of chemical reaction mass kinetics. From this recover linearized close to equilibrium and analyze global-in-time well-posedness small initial data critical Besov space.

We construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on (0, 1)n that have vanishing normals at the boundary. We give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping between a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor prod...

In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q differentiability, i.e. the main theorem isomorphism between solution space and data using Besov Triebel--Lizorkin spaces. The key compatibility conditions initial data. We are able to get unique smooth if satisfying smooth.

Besov as well as Sobolev spaces of dominating mixed smoothness are shown to be tensor products of Besov and Sobolev spaces defined on R. Based on this we derive several useful characterizations from the the one-dimensional case to the ddimensional situation. Finally, consequences for hyperbolic cross approximations, in particular for tensor product splines, are discussed.