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61.
62.
The paper is devoted to an application of a general local method of studying the Fredholmness of nonlocal bounded linear operators to Banach algebras of singular integral operators with piecewise continuous coefficients and discrete subexponential groups of piecewise smooth shifts acting topologically freely on composed contours. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
63.
Alexei Yu. Karlovich Lech Maligranda 《Proceedings of the American Mathematical Society》2001,129(9):2727-2739
In this paper we deal with the interpolation from Lebesgue spaces and , into an Orlicz space , where and for some concave function , with special attention to the interpolation constant . For a bounded linear operator in and , we prove modular inequalities, which allow us to get the estimate for both the Orlicz norm and the Luxemburg norm,
where the interpolation constant depends only on and . We give estimates for , which imply . Moreover, if either or , then . If , then , and, in particular, for the case this gives the classical Orlicz interpolation theorem with the constant .
64.
Yuri I. Karlovich Enrique Ramírez de Arellano 《Integral Equations and Operator Theory》2001,39(4):441-474
LetB be the Banach algebra of all bounded linear operators on the weighted Lebesgue spaceL
p (T, ) with an arbitrary Muckenhoupt weight on the unit circleT, and
the Banach subalgebra ofB generated by the operators of multiplication by piecewise continuous coefficients and the operatorse
h,S
T
e
h,
–1
I (hR, T) whereS
T is the Cauchy singular integral operator ande
h,(t)=exp(h(t+)/(t–)),tT. The paper is devoted to a symbol calculus, Fredholm criteria and an index formula for the operators in the algebra
and its matrix analogue
. These shift-invariant algebras arise naturally in studying the algebras of singular integral operators with coefficients admitting semi-almost periodic discontinuities and shifts being diffeomorphisms ofT onto itself with second Taylor derivatives.Partially supported by CONACYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México. 相似文献
65.
66.
67.
Alexei Yu. Karlovich Yuri I. Karlovich Amarino B. Lebre 《Integral Equations and Operator Theory》2011,71(1):29-53
Suppose α is an orientation-preserving diffeomorphism (shift) of
\mathbb R+=(0,¥){\mathbb {R}_+=(0,\infty)} onto itself with the only fixed points 0 and ∞. In Karlovich et al. (Integr Equ Oper Theory 2011, doi:) we found sufficient conditions for the Fredholmness of the singular integral operator with shift
(aI-bWa)P++(cI-dWa)P-(aI-bW_\alpha)P_++(cI-dW_\alpha)P_- 相似文献 |