Ideal properties of the Dunford integration operator

2015 ◽  
Vol 288 (11-12) ◽  
pp. 1207-1215 ◽  
Author(s):  
F. Bertoloto ◽  
G. Botelho ◽  
A. Jatobá
Keyword(s):  
Integration Operator

scholarly journals New proof of Nagnibida's theorem

2006 ◽  
Vol 4 (1) ◽  
pp. 85-90
Author(s):  
Mubariz T. Karaev
Keyword(s):  
Holomorphic Functions ◽  
Integration Operator

Using the Duhamel product for holomorphic functions we give a new proof of Nagnibida’s theorem on unicellularity of integration operatorJα,(Jαf)(z)=∫αzf(t)dt, acting in the spaceHoℓ(Ω).

scholarly journals A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Stefan Samko
Keyword(s):  
Fractional Integration ◽  
Fractional Integrals ◽  
Variable Order ◽  
Integration Operator ◽  
Hölder Continuous ◽  
Open Set ◽  
Fractional Integration Operator ◽  
Limiting Case

AbstractWe show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝn in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small order.

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