On some Properties of the ε-Product of Nuclear b-spaces
In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...
In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair of Banach function spaces is characterized, where and satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from into of the form is studied, where , , are prescribed functions under some local integrability conditions, the kernel is non-negative and is assumed to satisfy certain additional...
For 1 ≤ q ≤ α ≤ p ≤ ∞, is a complex Banach space which is continuously included in the Wiener amalgam space and contains the Lebesgue space . We study the closure in of the space of test functions (infinitely differentiable and with compact support in ) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space ) and obtain...