During the last 60 years the theory of function spaces has been a subject of growing interest
and increasing diversity. Based on three formally different developments, namely, the theory …

This article unifies the theory for Hardy spaces built on Banach lattices on ${\mathbb {R}}^ n
$ satisfying certain weak conditions on indicator functions of balls. The authors introduce a …

Both the real-variable theory of function spaces and the boundedness of operators are
always one of the core contents of harmonic analysis, while the Lebesgue spaces are the …

This book is the continuation of Local Function Spaces, Heat and Navier–Stokes Equations
(Tracts in Mathematics 20, 2013) by the author. A new approach is presented to exhibit …

In this article, the authors introduce Besov-type spaces with variable smoothness and
integrability. The authors then establish their characterizations, respectively, in terms of φ …

In this paper, the authors propose a new framework under which a theory of generalized
Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces …

There is a rapidly increasing number of papers dealing with smoothness spaces related to
Morrey spaces. It will be the aim of this survey to give an introduction to one of these …

In this paper, the authors establish new characterizations of the recently introduced Besov-
type spaces ̇B^s,τ_p,q(R^n) and Triebel-Lizorkin-type spaces ̇F^s,τ_p,q(R^n) with …

The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey
spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are …

We deal with the generalized Orlicz–Morrey space M ϕ, Φ (R n) M_ϕ,\varPhi(R^n) of the
third kind and consider the decomposition method. Also we characterize its predual space …