Year: 2026
Type: article
Abstract: In this paper, we prove that the fractional maximal operator $$M_\alpha $$ M α is bounded from the Orlicz-Lorentz space $$L_{\varPsi ,p}(\mathbb {R}^n)$$ L Ψ , p ( R n ) to the Orlicz-Lorentz space $$L_{\varPhi ,q}(\mathbb {R}^n)$$ L Φ , q ( R n ) , where $$n\in \mathbb {N}$$ n ∈ N , $$0\le \alpha 0 ≤ α < n , $$0 0 < p ≤ q ≤ ∞ , $$\varPhi $$ Φ is an Orlicz function of upper type $$p_{\varPhi }\in (0,\infty )$$ p Φ ∈ ( 0 , ∞ ) and $$\varPsi $$ Ψ is an Orlicz function of lower type $$p_{\varPsi }\in (1,\infty )$$ p Ψ ∈ ( 1 , ∞ ) . During the proof of the result, we have essentially used an inequality for the non-increasing rearrangement of the fractional maximal operator. Moreover, we also present several novel characterizations of Campanato type spaces by means of commutators of the fractional maximal operator. As an application, some conditions implying the Fefferman-Stein vector-valued inequalities for fractional maximal operator and its commutators on Orlicz-Lorentz spaces are established. The results obtained are substantial improvements and extensions of some known results.
Authors: Zhiwei Hao, Qianjun He, Mei Li, Ferenc Weisz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,590
Funders: National Natural Science Foundation of China, Eötvös Loránd Tudományegyetem, Beijing Information Science and Technology University, Scientific Research Foundation of Hunan Provincial Education Department, National Outstanding Youth Science Fund Project of National Natural Science Foundation of China
Awards: G4339800966, G7762100434, G8504923454
OpenAlex ID: W7160864904