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,∞), q∈[1,∞), α∈ ℝ, and s be a non-negative integer. Inspired by the
space JN p introduced by John and Nirenberg (1961) and the space ℬ introduced by …

Let p ∈ 1, ∞ p∈ 1,∞, q ∈ (1, ∞) q∈(1,∞), s ∈ Z _+:= N ∪ {0\} s∈ Z+:= N∪ 0, and α ∈ R
α∈ R. In this article, the authors introduce a reasonable version TT~ of the Calderón …

We study a function space JN p based on a condition introduced by John and Nirenberg as
a variant of BMO. It is known that L p⊂ JN p⊊ L p,∞, but otherwise the structure of JN p is …

Abstract Let p∈[1,∞], q∈[1,∞), s∈ Z+:= N∪{0}, α∈ R, and β∈(0, 1). In this article, the
authors first find a reasonable version I~ β of the (generalized) fractional integral I β on the …

In this article, via combining Riesz norms with Morrey norms, the authors introduce and
study the so-called Riesz–Morrey space, which differs from the John–Nirenberg …

Abstract Let p∈(1,∞), q∈[1,∞), α∈[0,∞) and s be a non-negative integer. In this article, the
authors introduce the John–Nirenberg–Campanato space JN (p, q, s) α (X), where X is R n …

There still exist many unsolved problems on the study related to John–Nirenberg spaces. In
this article, the authors introduce two new vanishing subspaces of the John–Nirenberg …

Abstract The John–Nirenberg spaces JN p are generalizations of the space of bounded
mean oscillation BMO with JN∞= BMO. Their vanishing subspaces VJN p and CJN p are …

Our main result is an abstract good-λ inequality that allows us to consider three self-
improving properties related to oscillation estimates in a very general context. The novelty of …