In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Let L be a divergence form inhomogeneous higher order elliptic operator with complex bounded measurable coefficients. In this article, for all p ∈ (0, ∞) and L satisfying a weak ellipticity condition, the authors introduce the local Hardy spaces hpL(R ) associated with L, which coincide with Goldberg’s local Hardy spaces h(R) for all p ∈ (0, ∞) when L ≡ −∆ (the Laplace operator). The authors al...

Abstract. This paper presents new sequence spacesX(r, s, t, p;B) forX ∈ {l∞(p), c(p), c0(p), l(p)} defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces X(r, s, t, p;B) for X ∈ {c(p), c0(p), l(p)} have Schauder basis. Furthermore, the α-, β-, γduals of these sequence spaces are computed and also obtained necessary...

We present a new scale U p (s < −t < 0 and 1 ≤ p < ∞) of anisotropic Banach spaces, defined via Paley–Littlewood, on which the transfer operator Lgφ = (g · φ) ◦ T−1 associated to a hyperbolic dynamical system T has good spectral properties. When p = 1 and t is an integer, the spaces are analogous to the “geometric” spaces Bt,|s+t| considered by Gouëzel and Liverani [26]. When p > 1 and −1 + 1/p...

where Sn is the unit sphere {(η,ξ) ∈R×Rn : η2 +‖ξ‖2 = 1} in Rn+1 and σn is the surface measure on Sn normalized to have total measure one. This operator plays an important role and has many applications, for example, in image processing of so-called synthetic aperture radar (SAR) data (see [7, 8]), or in the linearized inverse scattering problem in acoustics [6]. In [10], the authors associate ...