Boundedness of the maximal operator in the local Morrey-Lorentz spaces

Abstract

In this paper we define a new class of functions called local Morrey-Lorentz spaces M loc p,q;λ (R n ), 0 < p, q ≤ ∞ and 0 ≤ λ ≤ 1. These spaces generalize Lorentz spaces suchis trivial, and in the limiting case λ = 1, the space M loc p,q;1 (R n ) is the classical Lorentz spaceWe show that for 0 < q ≤ p < ∞ and 0 < λ ≤

$B-$ Riezs potential in $B-$ local Morrey-Lorentz spaces

“…have been studied by many researchers [3,4,[10][11][12][13][14][15]21]. The Riesz potential connected with the Laplace-Bessel differential operator (B−Riesz potential) is generated by generalized shift operator…”

Maximal and Calderon-Zygmund operators on the local variable Morrey-Lorentz spaces and some applications

“…The Lorentz-Morrey space L p,q;λ (R n ) was first defined in [27] and also considered in [16,17,28]. Later, the local Morrey-Lorentz spaces M loc p,q;λ (R n ) are introduced and the basic properties of these spaces are given in [1]. These spaces are a very natural generalization of the Lorentz spaces such that M loc p,q;0 (R n ) = L p,q (R n ).…”

Definability of singular integral operators on Morrey–Banach spaces

“…Recently, the studies of Morrey spaces is extending to Morrey space built on some non Lebesgue spaces such as Morrey-Lorentz spaces [3,18,31], Orlicz-Morrey spaces [11,29,28], Morrey spaces with variable exponents [1,13,15,19,22,24,25,26,33,32]. On the other hand, for instance, in [15,19], we are lack of a precise definition of the action of singular integral operators on the above mentioned Morrey type spaces.…”