In this survey, we discuss the definition of a (quasi-) Banach function space. We advertise
the original definition by Zaanen and Luxemburg, which does not have various issues …

Abstract Let (χ, ρ, μ) be a space of homogeneous type in the sense of Coifman and Weiss,
and Y (χ) a ball quasi-Banach function space on χ, which supports both a Fefferman-Stein …

The real-variable theory of function spaces has always been at the core of harmonic
analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of …

Let X be a ball quasi-Banach function space on R n. In this article, the authors first cleverly
introduce some new ball Campanato-type function spaces associated with X. Then, under …

In this systematic review, the authors give a survey on the recent developments of both the
John–Nirenberg space JN p and the space BMO as well as their vanishing subspaces such …

Abstract Let p∈[1,∞) and X be a ball Banach function space on R n with an absolutely
continuous norm for which the Hardy–Littlewood maximal operator is bounded on (X 1/p) …

Let γ∈ ℝ∖{0} and X (ℝ n) be a ball Banach function space satisfying some extra mild
assumptions. Assume that Ω= ℝ n or Ω⊂ ℝ n is an (𝜀,∞)-domain for some 𝜀∈(0, 1]. In this …

Let X be a ball Banach function space on R n. In this article, under some mild assumptions
about both X and the boundedness of the Hardy–Littlewood maximal operator on the …

Let X be a ball quasi-Banach function space on R n. In this article, under some mild
assumptions about both X and the boundedness of the Hardy–Littlewood maximal operator …

Let X be a ball quasi-Banach function space on R n and HX (R n) the associated Hardy
space. In this article, under the assumptions that the Hardy–Littlewood maximal operator …