Publications

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In Press
Fernandes, Cláudio A., Alexei Yu. Karlovich, and Yuri I. Karlovich. "Calkin images of Fourier convolution operators with slowly oscillating symbols." Proceedings of IWOTA 2019. In Press.
Fernandes, Cláudio A., Alexei Yu. Karlovich, and Yuri I. Karlovich. "Fourier convolution operators with symbols equivalent to zero at infinity on Banach function spaces." Proceedings of ISAAC 2019. In Press.
Canarias, Tiago, Alexei Karlovich, and Eugene Shargorodsky. "Multiplication Is an open bilinear mapping in the Banach algebra of functions of bounded Wiener $p$-variation." Real Analysis Exchange (In Press).
Fernandes, Cláudio A., and Alexei Yu. Karlovich. "Semi-almost periodic Fourier multipliers on rearrangement-invariant spaces with suitable Muckenhoupt weights." Boletín de la Sociedad Matemática Mexicana (In Press).
Karlovich, Alexei Yu. "Wavelet bases in Banach function spaces." Bulletin of the Malaysian Mathematical Sciences Society (In Press).Website
2020
Karlovich, Alexei Yu. "Algebras of continuous Fourier multipliers on variable Lebesgue spaces." Mediterranean Journal of Mathematics. 17.102 (2020): 19 pages.Website
Karlovich, Alexei Yu. "Hardy-Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type." Studia Mathematica. 254.2 (2020): 149-178.
Bastos, Maria Amélia, Luís Castro, and Alexei Yu. Karlovich(eds.) Operator Theory, Functional Analysis and Applications. Basel: Birkhäuser, 2020.
2019
Fernandes, Cláudio A., Alexei Yu. Karlovich, and Yuri. I. Karlovich. "Algebra of convolution type operators with continuous data on Banach function spaces." Banach Center Publications. 119 (2019): 157-171.Website
Karlovich, Alexei, and Eugene Shargorodsky. "The Brown-Halmos theorem for a pair of abstract Hardy spaces." Journal of Mathematical Analysis and Applications. 472 (2019): 246-265.Website
Karlovich, Alexei Yu. "Hardy-Littlewood maximal operator on the associate space of a Banach function space." Real Analysis Exchange. 44.1 (2019): 119-140.Website
Fernandes, Cláudio A., Alexei Yu. Karlovich, and Yuri I. Karlovich. "Noncompactness of Fourier convolution operators on Banach function spaces." Annals of Functional Analysis. 10.4 (2019): 553-561.
Karlovich, Alexei Yu., and Eugene Shargorodsky. "When does the norm of a Fourier multiplier dominate its L-infinfty norm?" Proceedings of the London Mathematical Society. 118 (2019): 901-941.Website
2018
Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "Criteria for n(d)-normality of weighted singular integral operators with shifts and slowly oscillating data." Proceedings of the London Mathematical Society. 116.4 (2018): 997-1027 .Website
Karlovich, Alexei Yu., and Eugene Shargorodsky. "More on the density of analytic polynomials in abstract Hardy spaces." The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, vol. 268. Eds. Albrecht Böttcher, Daniel Potts, Peter Stollman, and David Wenzel. Basel: Birkhäuser, 2018. 319-329.
André, Carlos, Maria Amélia Bastos, Alexei Yu. Karlovich, Bernd Silbermann, and Ion Zaballa(Eds.) Operator Theory, Operator Algebras, and Matrix Theory. Basel: Birkhäuser, 2018.Website
Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "Semi-Fredholmness of weighted singular integral operators with shifts and slowly oscillating data." Operator Theory, Operator Algebras, and Matrix Theory. Operator Theory: Advances and Applications, vol. 267. Eds. Carlos André, Maria Amélia Bastos, Alexei Yu. Karlovich, Bernd Silbermann, and Ion Zaballa. Basel: Birkhäuser, 2018. 221-246.
2017
Karlovich, Alexei Yu. "Density of analytic polynomials in abstract Hardy spaces." Commentationes Mathematicae. 57.2 (2017): 131-141.Website
Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "The index of weighted singular integral operators with shifts and slowly oscillating data." Journal of Mathematical Analysis and Applications. 450 (2017): 606-630.Website
Bini, Dario, Torsten Ehrhardt, Alexei Yu. Karlovich, and Ilya M. Spitkovsky(eds.) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. The Albrecht Böttcher Anniversary Volume. Basel: Birkhäuser Basel, 2017.Website
Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "Necessary Fredholm conditions for weighted singular integral operators with shifts and slowly oscillating data." Journal of Integral Equations and Applications. 29.3 (2017): 365-399.
Karlovich, Alexei Yu. "Toeplitz operators on abstract Hardy spaces built upon Banach function spaces." Journal of Function Spaces. 2017 (2017): Article ID 9768210, 8 pages.Website
2016
Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "The generalized Cauchy index of some semi-almost periodic functions." Boletín de la Sociedad Matemática Mexicana. 22.2 (2016): 473-485. AbstractWebsite

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 oscillating data.

Karlovich, Alexei Yu., Yuri I. Karlovich, and Amarino B. Lebre. "On a weighted singular integral operator with shifts and slowly oscillating data." Complex Analysis and Operator Theory. 10.6 (2016): 1101-1131. AbstractWebsite

Let \(\alpha,\beta\) be orientation-preserving diffeomorphism (shifts) of \(\mathbb{R}_+=(0,\infty)\) onto itself with the only fixed points \(0\) and \(\infty\) and \(U_\alpha,U_\beta\) be the isometric shift operators on \(L^p(\mathbb{R}_+)\) given by \(U_\alpha f=(\alpha')^{1/p}(f\circ\alpha)\), \(U_\beta f=(\beta')^{1/p}(f\circ\beta)\), and \(P_2^\pm=(I\pm S_2)/2\) where \[ (S_2 f)(t):=\frac{1}{\pi i}\int\limits_0^\infty \left(\frac{t}{\tau}\right)^{1/2-1/p}\frac{f(\tau)}{\tau-t}\,d\tau, \quad t\in\mathbb{R}_+, \]
is the weighted Cauchy singular integral operator. We prove that if \(\alpha',\beta'\) and \(c,d\) are continuous on \(\mathbb{R}_+\) and slowly oscillating at \(0\) and \(\ infty\), and \[ \limsup_{t\to s}|c(t)|<1,\quad \limsup_{t\to s}|d(t)|<1, \quad s\in\{0,\infty\}, \] then the operator \((I-cU_\alpha)P_2^++(I-dU_\beta)P_2^-\) is Fredholm on \(L^p(\mathbb{R}_+)\) and its index is equal to zero. Moreover, its regularizers are described.