Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

where the unknown are u, θ, π which denote, respectively, the velocity field, the scalar temperature and the scalar pressure. Data are the positive constants ν, χ, respectively, the viscosity and the thermal conductivity coefficients and the function f the external force field, and a(x), b(x), respectively, represent the initial velocity and initial temperature. The main objective of this work ...

We establish a family of inequalities that allow one to estimate the Lq-norm matrix-valued field by an elliptic part and Lp-norm curl. This particularly extends previous work Neff et al. and, as main novelty, is applicable in regime p=1.

For p ∈ R, the generalized logarithmic mean Lp a, b , arithmetic mean A a, b and geometric mean G a, b of two positive numbers a and b are defined by Lp a, b a, a b; Lp a, b a 1 − b 1 / p 1 a − b , p / 0, p / − 1, a/ b; Lp a, b 1/e b/a 1/ b−a , p 0, a/ b; Lp a, b b − a / ln b − lna , p −1, a/ b; A a, b a b /2 and G a, b √ ab, respectively. In this paper, we give an answer to the open problem: f...

In this article, the authors present a new Lp-primal–dual weak Galerkin method (Lp-PDWG) for convection–diffusion equations. Comparing with standard L2-PDWG method, solution calculated from Lp-PDWG may exhibit some important advantages and features (e.g., less jumps cross element interface when p?1, or sparsity by using p=1 wavelet basis approximation). The existence uniqueness of numerical is ...

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.

We consider the Navier-Stokes equations in exterior domains and in the weighted L space. For this purpose, we consider the L − L estimates of Stokes semigroup with weight 〈x〉 type. Our proof is based on the cut-off technique with local energy decay estimate proved by Dan, Kobayashi and Shibata [1] and the weighted L − L estimates of Stokes semigroup in the whole space proved by Kobayashi and Ku...

This paper addresses the problem of simultaneous sparse approximation of signals, given an overcomplete dictionary of elementary functions, with a joint sparsity profile induced by a lp − lq mixednorm. Our contributions are essentially two-fold i) making connections between such an approach and other methods available in the literature and ii) on providing algorithms for solving the problem wit...

We introduce the class of doubly atomless bands in Lp(Lq)-Banach lattices and show that this class is axiomatizable by positive bounded sentences in the language of Banach lattices. (Here p 6= q are fixed and in the interval 1 ≤ p, q < ∞ .) The theory of this class is complete (indeed, we show it is separably categorical) and model complete. Further, we show that it satisfies quantifier elimina...