Function Spaces

Pick, Luboš; Kufner, Alois; John, Oldřich; Fučík, Svatopluk

doi:10.1515/9783110250428

Cited by 104 publications

(114 citation statements)

References 0 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…The ideas of Morrey [11] were further developed by Campanato [13]. A more systematic study of these (and even more general) spaces, we refer the readers to see [12,[14][15][16][17][18][19][20][21]. In 1964, Beurling [22] first introduced some fundamental forms of Herz spaces to study convolution algebras.…”

Section: Preliminaries and Main Lemmasmentioning

confidence: 99%

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Yang

Tao

2017

Journal of Function Spaces

View full text Add to dashboard Cite

Let be the singular integral operator with variable kernel defined by ( ) = p.v. ∫ R (Ω( , − )/| − | ) ( )d and let (0 ≤ ≤ 1) be the fractional differentiation operator. Let * and ♯ be the adjoint of and the pseudoadjoint of , respectively. In this paper, the authors prove that − and ( * − ♯ ) are bounded, respectively, from Morrey-Herz spaceṡ, ,1 (R ) to the weak Morrey-Herz spaceṡ, ,1 (R ) by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product 1 2 and the pseudoproduct 1 ∘ 2 are also given.

show abstract

Section: Preliminaries and Main Lemmasmentioning

confidence: 99%

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Yang

Tao

2017

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…In the following, we give the definitions and list some results regarding Banach Function Spaces, see Bennett and Sharpley [1] and Pick, Kufner, John, and Fučík [56] for the proofs. …”

Section: Banach Function Spacesmentioning

confidence: 99%