Predual Spaces of Morrey Spaces with Non-doubling Measures

Abstract

In this paper under some growth condition we investigate the connection between RBMO and the Morrey spaces. We do not assume the doubling condition which has been a key property of harmonic analysis. We also obtain another type of equivalent norms.

Generalized weighted Morrey spaces and classical operators

“…The definition given here is close to the one in [, (3.1)]. There is another definiton by means of the predual [, p. 483]; see for more recent information.…”

The Hardy Space H1 with Non-doubling Measures and Their Applications

“…Then, the authors in [116] considered several classical operators, e. g. the maximal operator or the fractional integral operator, and investigated the boundedness of these operators in the Morrey spaces. Sawano and Takana in [117] further investigated the connection between RBMO . / and the Morrey spaces, and in [120] investigated the predual of the Morrey spaces.…”

“…Sawano and Takana in [117] further investigated the connection between RBMO . / and the Morrey spaces, and in [120] investigated the predual of the Morrey spaces. …”

Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

“…These investigations were also elaborated and continued in collaboration with S. Roch (Darmstadt) and B. Silbermann (Chemnitz) in the papers [136] (1998), [137,138] (2001), [113] (2002), [114][115][116] (2003), [117] (2004), [124,125] (2007), [141] (2008) and in his papers [95][96][97] (2003), [98] (2004).…”

“…for 1 < 1 < 2 < ∞, see formula (3) in [96]. In [96] there was also made a comparison of the space M (2, ) with the space M (1, ), the latter being defined with the usage of cubes which only satisfy the condition ( ) ≤ ( ) with > − where > 1 is fixed and the measure does not necessarily satisfies the growth condition or the doubling condition.…”