Orlicz–Morrey Spaces and Fractional Operators

Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces

“…The definition of Orlicz-Morrey spaces introduced in [7] and used here is different from that of the papers [24], [34] and other papers.…”

“…Such spaces were studied in [24] first, see also [7,13,25,26,34]. The most general spaces of such a type, MusielakOrlicz-Morrey spaces, unifying the classical and variable exponent approaches, were an object of study in [22], where potential operators were studied.…”

Commutators of parametric Marcinkiewicz integrals on generalized Orlicz-Morrey spaces

“…Various versions of generalized Orlicz-Morrey spaces were introduced in [14], [15] and [2]. We used the de…nition of [2] which runs as follows.…”

“…In words of [10], our generalized Orlicz-Morrey space is the third kind and the ones in [14] and [15] are the …rst kind and the second kind, respectively. According to the examples in [6], one can say that the generalized Orlicz-Morrey spaces of the …rst kind and the second kind are di¤erent and that the second kind and the third kind are di¤erent.…”

A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz–Morrey spaces

“…Such spaces were first introduced and studied by Nakai [6]. Then another kind of generalized Orlicz-Morrey spaces were introduced by Sawano et al [7]. The generalized Orlicz-Morrey spaces used in this paper was introduced in [8].…”