Variable exponent Campanato spaces

Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

“…In the latter result, the proof of the embedding of Morrey spaces into Campanato spaces was based on the notion of (⋅)-average of a function introduced in this paper. Similar results for variable exponent Campanato spaces L (⋅), (⋅) ( ) in a more general setting of metric measure spaces were obtained in H. Rafeiro and S. Samko [90] (2011). In [90], in the setting of an arbitrary quasimetric measure spaces, the log-Hölder condition for ( ) is introduced with the distance ( , ) replaced by ( , ( , )), which provides a weaker restriction on ( ) in the general setting.…”

“…Similar embedding theorem for variable Campanato spaces may be found in [90] (2011) within the frameworks of the general setting of metric measure spaces. V. Kokilashvili and A. Meskhi [58] (2008), see also [59] (2010), introduced Morrey-type spaces (⋅) (⋅) in the general setting when the underlying space is a homogeneous-type space ( , , ), with the norm defined by…”

“…Rabinovich in fact turned this approach into a powerful general method, nowadays known as the "method of limit operators" by extending it and giving its wide applications to the investigation of the Fredholm properties of pseudodifferential operators, convolution type operators on ℤ and ℝ , general boundary values problems of the Boutet de Monvel type on manifolds with conical structure at infinity and pseudodifferential operators with shifts, etc, in his paper [61] (1985) and in the series of his papers [22,24] (1985) and [25] (1986) with the Ph.D. student B. Lange and later in his papers [73] (1992), [76] (1993), [77] (1994), [84] (1998), [87] (1999) and [89,90] (2001).…”

Derivative and Lipschitz Type Characterizations of Variable Exponent Bergman Spaces

“…By the remark 1 in [18], we have that ∈ 0 . By Lemma 15 we conclude that the family F = {( , ) : ∈ 0 (B )} satisfies (17). By the fact that ( (⋅)/ 0 ) ∈ P log (B )…”

“…The following Jensen type inequality was proved in [17] in the context of spaces of homogeneous type (SHT).…”