# Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts

@article{Karlovich2014FredholmnessAI,
title={Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts},
author={Alexei Yu. Karlovich},
journal={arXiv: Functional Analysis},
year={2014}
}
• A. Karlovich
• Published 2 May 2014
• Mathematics
• arXiv: Functional Analysis
Let $\alpha$ and $\beta$ be orientation-preserving diffeomorphisms (shifts) of $\mathbb{R}_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$, where the derivatives $\alpha'$ and $\beta'$ may have discontinuities of slowly oscillating type at $0$ and $\infty$. For $p\in(1,\infty)$, we consider the weighted shift operators $U_\alpha$ and $U_\beta$ given on the Lebesgue space $L^p(\mathbb{R}_+)$ by $U_\alpha f=(\alpha')^{1/p}(f\circ\alpha)$ and $U_\beta f= (\beta')^{1/p}(f\circ… 6 Citations • Mathematics • 2018 Let α, β be orientation-preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞, and whose restrictions to ℝ+ = (0,∞) are diffeomorphisms, and let Uα, Uβ be the • Mathematics • 2014 We study Mellin pseudodifferential operators (shortly, Mellin PDO's) with symbols in the algebra$\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))\$ of slowly oscillating functions of limited
• Mathematics
• 2018
Let α,β be orientation‐preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞ , and whose restrictions to R+=(0,∞) are diffeomorphisms, and let Uα,Uβ be the
• Mathematics
• 2016
We compute the generalized Cauchy index of some semi-almost periodic functions, which are important in the study of the Fredholm index of singular integral operators with shifts and slowly
• Mathematics
Boletín de la Sociedad Matemática Mexicana
• 2016
We compute the generalized Cauchy index of some semi-almost periodic functions, which are important in the study of the Fredholm index of singular integral operators with shifts and slowly

## References

SHOWING 1-10 OF 36 REFERENCES

• Mathematics
• 2010
Suppose α is an orientation-preserving diffeomorphism (shift) of $${\mathbb {R}_+=(0,\infty)}$$ onto itself with the only fixed points 0 and ∞. In Karlovich et al. (Integr Equ Oper Theory 2011,
• Mathematics
• 2011
Suppose α is an orientation preserving diffeomorphism (shift) of $${{\mathbb{R}}_+=(0,\infty)}$$ onto itself with the only fixed points 0 and ∞. We establish sufficient conditions for the
• Mathematics
• 2013
Let $${\mathcal{B}_{p,w}}$$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space $${L^p(\mathbb{R},w)}$$ , where $${p\in(1,\infty)}$$ and w is a Muckenhoupt
• Mathematics
• 2012
Let $${\mathcal{B}_{p,w}}$$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space $${L^{p}(\mathbb{R}, w)}$$, where $${p \in (1, \infty)}$$ and w is a
• Mathematics
• 2013
The aim of this work is to study a singular integral operator $${\mathbf{A}=aI+bS_\Gamma}$$A=aI+bSΓ with the Cauchy operator SΓ (SIO) and Hölder continuous coefficients a, b in the space
Let V (ℝ) denote the Banach algebra of absolutely continuous functions of bounded total variation on ℝ. We study an algebra $$\mathfrak{B}$$ of pseudodifferential operators of zero order with
Using the boundedness of the maximal singular integral operator related to the Carleson-Hunt theorem we prove the boundedness and study the compactness of pseudo-differential operators a(x,D) with
Let VR denote the Banach algebra of absolutely continuous functions of bounded total variation on R, and let Bp be the Banach algebra of bounded linear operators acting on the Lebesgue space LpR for
• Mathematics
• 1992
1 The operator of singular integration.- 1.1 Notations, definitions and auxiliary statements.- 1.1.1 The operator of singular integration.- 1.1.2 The space Lp(?,?).- 1.1.3 Interpolation theorems.-