In this article, the authors completely answer an open question, presented in Tao et al. [A bridge connecting Lebesgue and Morrey spaces via Riesz norms. Banach J Math Anal. 2021;15(1):20], showing that Riesz–Morrey space is truly a new larger than particular with critical index. Indeed, just real interpolation of for suitable indices. Moreover, further show aforementioned inclusion also proper...

*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...

In this paper we consider the Spanne type boundedness of sublinear operators and prove the Adams type boundedness theorems for these operators and also give BMO (bounded mean oscillation space) estimates for their commutators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are formulated in terms of Zygmund type integral inequalities. Based on the properties of the...

Abstract We prove weighted boundedness of Calderón–Zygmund and maximal singular operators in generalized Morrey spaces on quasi-metric measure spaces, general non-homogeneous, only under the growth condition measure, for a certain class weights. Weights characteristic are independent each other. Weighted operator is also proved case when lower upper Ahlfors exponents coincide with Our approach ...

Abstract We consider the singular limit problem for Cauchy of (Patlak–) Keller–Segel system parabolic-parabolic type. The is considered in uniformly local Lebesgue spaces and as relaxation parameter $$\tau $$ τ goes to infinity, solution equation converges a drift-diffusion strong topology. For proof, we foll...

We study embeddings between generalised Besov–Morrey spaces Nφ,p,qs(Rd). Both sufficient and necessary conditions for the are proved. Embeddings of into Lebesgue Lr(Rd) also considered. Our approach requires a wavelet characterisation which we establish system Daubechies wavelets.

In this paper, we establish necessary and sufficient conditions for boundedness of m-linear p-adic integral operators with general homogeneous kernel on Lebesgue spaces Morrey spaces, respectively. each case, obtain the corresponding operator norms. Also, deal some particular examples compare them previously known from literature.