Dual spaces of local Morrey-type spaces

Abstract

In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.

Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent

“…This corollary gives a characterization of Morrey spaces of variable exponents; see also the paper by Gogatishvili and Mustafayev [19] for constant exponents.…”

“…Next, following Di Fratta-Fiorenza [17] and Gogatishvili-Mustafayev [19] , we study the duality properties among those Herz-Morrey spaces. In particular, we show the associate spaces of H…”

“…For related results, we refer the reader to the paper by Di Fratta and Fiorenza [17] with logarithmic weights, and the paper by Gagatishvili and Mustafayev [19] with general weights.…”

New pre-dual space of Morrey space

“…In [5] the associate spaces of local Morrey-type and complementary local Morrey-type spaces were calculated. Our method of construction of the pre-dual space of the Morrey space mainly based on these results.…”

“…In [5] it is proved that the space LM p ′ θ ′ , ω is dual space of the space LM pθ ,ω , where 1 ≤ p, θ < ∞, p ′ and θ ′ are conjugate exponents of p and θ , respectively, and  ω(t) = ω θ−1 (t)  ∞ t ω θ (s)ds  −1 (see Theorem 3.6 below).…”