Generalized fractional integral operators on vanishing generalized local Morrey spaces

Abstract

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator I ρ from the vanishing generalized local Morrey spaces V LM {x 0 } p,ϕ 1 to V LM {x 0 } q,ϕ 2 , 1 < p < q < ∞, and from the space V LM {x 0 } 1,ϕ 1 to the weak space V W LM {x 0 } q,ϕ 2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator I ρ from the vanishing generalized Morrey spaces V M p,ϕ

Maximal and fractional maximal operators in the Lorentz Morrey spaces and their applications to the Bochner Riesz and Schrodinger type operators

“…Morrey spaces appeared to be useful in the study of local behavior properties of the solutions of second order elliptic PDEs. For more information about Morrey-type spaces see [5,6,10,13] and [14].…”

Two type Estimates for the Boundedness of Generalized Riesz Potential Operator in the Generalized Weighted Local Morrey Spaces

“…During the last decades, the theory of boundedness of classical operators of the harmonic analysis in the generalized Morrey spaces M p,ϕ (R n ) have been well studied by now, we refer the readers to [9,14,15,21] and [23].…”

“…Nakai [22] proved the boundedness of I ρ from the generalized Morrey spaces M 1,ϕ (R n ) to the spaces M 1,ψ (R n ) for suitable functions ϕ and ψ. The boundedness of I ρ from the generalized Morrey spaces M p,ϕ (R n ) to the spaces M q,ψ (R n ) is studied by Eridani [5], Guliyev et al [9], Kucukaslan et al [14,15], Kucukaslan [16,17], Nakai [23] and Nakamura [24].…”

Generalized fractional maximal operator on generalized local Morrey spaces

“…Nakai [22] proved the boundedness of the operators I and M from the generalized Morrey spaces M p;' 1 to the spaces M q;' 2 for suitable functions ' 1 and ' 2 . The boundedness of M and I from the generalized Morrey spaces M p;' 1 to the spaces M q;' 2 is studied by Nakai [23], Eridani [10], Gunawan [18], Eridani, Gunawan and Nakai [12], Sawano, Sugano, Tanaka [25], Eridani, Gunawan, Nakai, Sawano [11], Guliyev, Ismayilova, Kucukaslan, Serbetci [17], Kucukaslan, Hasanov, Aykol [19].…”

“…Nakai [28] proved the boundedness of I ρ and M ρ from the generalized Morrey spaces M 1,ϕ 1 to the spaces M 1,ϕ 2 for suitable functions ϕ 1 and ϕ 2 . The boundedness of I ρ and M ρ from the generalized Morrey spaces M p,ϕ 1 to the spaces M q,ϕ 2 are studied by Eridani et al [7][8][9], Guliyev et al [17], Gunawan [18], Kucukaslan et al [20,21,27], Kucukaslan [22], Nakai [29,30], Nakamura [31], Sawano et al [34,35] and Sugano [36].…”