ON GENERALIZED FRACTIONAL INTEGRALS

By E. Nakai. 2001

115 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a92bc749e905e4251a3b14ed049225b80a7d7e48

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In Applied Mathematics

Citations in the corpus

Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials (2010, background): “For the boundedness of Iρf , we also refer the reader to [14, 15, 7, 6, 17].”
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “Notice also that Nakai [27, 28] introduced a class of generalized fractional integrals and obtained their boundedness on Orlicz spaces over R with the d-dimensional Lebesgue measure and also over spaces of homogeneous type.”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, unknown): “The generalized fractional integral operators Iρ with ρ : (0,∞) → (0,∞) are studied in [144, 145, 146, 149, 206, 207] and the spaces L(R) with constant p and φ : R × (0,∞) → (0,∞) are studied in [142, 147, 151, 157].”
Orlicz–Morrey spaces and the Hardy–Littlewood maximal function (2008, background): “For generalized fractional integral operators, see also [32, 23, 24, 25, 6, 7, 11, 8].”
Weighted Hardy and singular operators in Morrey spaces (2008, background): “1 Introduction The well known Morrey spaces L introduced in [30] in relation to the study of partial differ ential equations, and presented in various books, see [18], [26], [47], were widely investigated during last decades, including the study of classical opera tors of harmonic analysis - maximal”
ON GENERALIZED FRACTIONAL INTEGRAL OPERATORS (2004, background): “For a general function ρ, Nakai [8, 9] proved that T̃ρ is bounded from L1,φ to L1,ψ for appropriate functions φ and ψ.”
Fractional Integrals and Generalized Olsen Inequalities (2009, background): “Let Tρ be the generalized fractional integral operator associated to a function ρ : (0,∞)→ (0,∞), as defined in [16].”
Orlicz–Morrey Spaces and Fractional Operators (2012, background): “In [8] Nakai studied the boundness of the generalized fractional integral operator Tρ on Orlicz spaces.”