Fractional integral operators on central Morrey spaces

Abstract

Abstract. We consider the boudedness of fractional integral operators on localized (central) Morrey spaces and investigate the relation between the Adams inequality and the Spanne inequality.Mathematics subject classification (2010): 42B20, 42B25.

Hardy’s inequalities and integral operators on Herz-Morrey spaces

“…The reader is referred to [3][4][5] for the studies of central Morrey spaces. We use the de nition of central Morrey spaces from [5, De nition 2] while we use the notion for the central Morrey spaces from [3,4].…”

“…Herz-Morrey spaces are extensions of Herz spaces [1] and Morrey spaces [2]. They also include the central Morrey spaces [3][4][5][6]. One of the pioneer studies on the Herz-Morrey spaces is from Lu and Xu [7] on the mapping properties of the singular integral operators on the Herz-Morrey spaces.…”

Two-weight norm inequalities for some fractional type operators related to Schrödinger operator on weighted Morrey spaces

“…Two-weight norm inequalities for the linear and multilinear fractional maximal operators and fractional integral operators on Lebesgue spaces were widely study; see [14,[16][17][18][19]. The weighted estimates with Muckenhoupt A p weights on Morrey spaces were studies in [12,20].…”

Weighted estimates for fractional integral operators on central Morrey spaces

“…On the contrary, to investigate the local behavior of solutions to second order elliptic differential equations, Adams proved the boundedness of fractional integral operators on Morrey spaces, and the authors obtained the boundedness on central Morrey spaces. The ordinary Morrey spaces and central Morrey spaces are defined as follows.…”

“…Remark is bounded from to (see ), but not bounded from to in general (see ).…”