Fractional integrals and singular integrals in the holder classes of variable order

1994 ◽  
Vol 2 (2) ◽  
pp. 91-106 ◽  
Author(s):  
N.K. Karapetyants ◽  
A.I Ginsburg
Keyword(s):  
Singular Integrals ◽  
Fractional Integrals ◽  
Variable Order ◽  
Hölder Classes ◽  
Holder Classes

Fractional Integrodifferentiation in Hölder Classes of Arbitrary Order

1995 ◽  
Vol 2 (2) ◽  
pp. 141-150
Author(s):  
N. K. Karapetyants ◽  
A. I. Ginzburg
Keyword(s):  
Fractional Integral ◽  
Arbitrary Order ◽  
Variable Order ◽  
Hölder Classes ◽  
Holder Classes ◽  
Fractional Integrodifferentiation

Abstract Hölder classes of variable order μ(x) are introduced and it is shown that the fractional integral has Hölder order μ(x) + α (0 < α, μ +, α + μ + < 1, μ + = sup μ(x)).

Hölder Classes in Lavrent'ev Domains

2004 ◽  
Vol 120 (5) ◽  
pp. 1791-1802
Author(s):  
N. A. Shirokov
Keyword(s):  
Hölder Classes ◽  
Holder Classes

The reserse Hölder classes in martingale setting

2004 ◽  
Vol 9 (3) ◽  
pp. 273-277
Author(s):  
Zuo Hong-liang ◽  
Liu Pei-de
Keyword(s):  
Hölder Classes ◽  
Holder Classes

A note on vanishing Morrey → VMO result for fractional integrals of variable order

2020 ◽  
Vol 23 (1) ◽  
pp. 298-302 ◽  
Author(s):  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Limiting Case

AbstractIn the limiting case of Sobolev-Adams theorem for Morrey spaces of variable order we prove that the fractional operator of variable order maps the corresponding vanishing Morrey space into VMO.

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