We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means ...

Tomographic reconstruction from limited X-ray data is an ill-posed inverse problem. A common Bayesian approach is to search for the maximum a posteriori (MAP) estimate of the unknowns that integrates the prior knowledge, about the nature of biomedical images, into the reconstruction process. Recent results on the Bayesian inversion have shown the advantages of Besov priors for the convergence o...

Let (R, μ) be a nonatomic finite measure space and E = Lr(R, μ) a Lebesgue space over R. Then we consider tempered distributions f and g (depending on x ∈ Rn and v ∈ R), for which divx(af) = g in S′(Rn, E). Here a : R −→ Rn is a bounded function of v (a velocity field) satisfying a nondegeneracy condition. We study the regularity of the average f̄ = R R f(·, v)ψ(v) dμ(v) ∈ S′(Rn) (with ψ ∈ Lr (R...

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space , the opti...

We study the Cauchy problem for quasi-geostrophic equations in a unit ball of two-dimensional space with homogeneous Dirichlet boundary condition. show existence and uniqueness strong solution framework Besov spaces. also establish spectral localization technique commutator estimates.

We verify that the $p$-integrable Teichmüller space $T_{p}$ admits canonical complex Banach manifold structure for any $p \geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of in terms $p$-Besov $p>1$.

Adaptive estimation of a quadratic functional over both Besov and Lp balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and Lp balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate ad...