The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted L spaces. Koosis’ theorem of 1980 gives a way to construct a certain class of pairs of weights. We show that Koosis’ theorem is closely related to (in fact, is a direct consequence of) a spectral perturbation model suggested by de B...

In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and Reich-Rus-Ciric type framework metric spaces, analyze existence points for such contractions equipped with some suitable hypotheses. A few consequences single-valued mappings which include conclusion main result Karapinar et al. [On Hard...

Let X be a ball quasi-Banach function space on $${{\mathbb {R}}}^n$$ and assume that the Hardy–Littlewood maximal operator satisfies Fefferman–Stein vector-valued inequality X, let $$q\in [1,\infty )$$ $$d\in (0,\infty . In this article, authors prove that, for any $$f\in {\mathcal {L}}_{X,q,0,d}({\mathbb {R}}^n)$$ (the Campanato-type associated with X), Littlewood–Paley g-function g(f) is eith...