Geodesic
Generalized fractional integrals in the vanishing generalized weighted local and global Morrey spaces
Filomat, Tome 37 (2023) no. 6, p. 1893

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DOI

In this paper, we prove the boundedness of generalized fractional integral operators I ρ in the vanishing generalized weighted Morrey-type spaces, such as vanishing generalized weighted local Morrey spaces and vanishing generalized weighted global Morrey spaces by using weighted L p estimates over balls. In more detail, we obtain the Spanne-type boundedness of the generalized fractional integral operators I ρ in the vanishing generalized weighted local Morrey spaces with w q ∈ A 1+ q p ′ for 1 p q ∞, and from the vanishing generalized weighted local Morrey spaces to the vanishing generalized weighted weak local Morrey spaces with w ∈ A 1,q for p = 1, 1 q ∞. We also prove the Adams-type boundedness of the generalized fractional integral operators I ρ in the vanishing generalized weighted global Morrey spaces with w ∈ A p,q for 1 p q ∞ and from the vanishing generalized weighted global Morrey spaces to the vanishing generalized weighted weak global Morrey spaces with w ∈ A 1,q for p = 1, 1 q ∞. The our all weight functions belong to Muckenhoupt-Weeden classes A p,q .
DOI : 10.2298/FIL2306893K
Classification : 42B20, 42B25, 42B35
Keywords: Generalized fractional integral operator, Vanishing generalized weighted local Morrey space, Vanishing generalized weighted global Morrey space, Muckenhoupt-Wheeden classes 
Abdulhamit Kucukaslan. Generalized fractional integrals in the vanishing generalized weighted local and global Morrey spaces. Filomat, Tome 37 (2023) no. 6, p. 1893 . doi: 10.2298/FIL2306893K
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     title = {Generalized fractional integrals in the vanishing generalized weighted local and global {Morrey} spaces},
     journal = {Filomat},
     pages = {1893 },
     year = {2023},
     volume = {37},
     number = {6},
     doi = {10.2298/FIL2306893K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2306893K/}
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