Publications

Export 2 results:
Sort by: Author Title Type [ Year (Desc)]
2018
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.
2004
Karlovich, Alexei Yu. "Some algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces." Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume. Operator Theory: Advances and Applications, 147. Eds. Israel Gohberg, Wolfgang Wendland, António Ferreira dos Santos, Frank-Ollme Speck, and Francisco Sepúlveda Teixeira. Basel: Birkhäuser, 2004. 287-296. Abstract

In this paper, the author proves that the set of all integrable functions whose sequences of negative (resp. nonnegative) Fourier coefficients belong to \(\ell^1\cap\ell^\Phi_{\varphi,w}\) (resp. to \(\ell^1\cap\ell^\Psi_{\psi,\varrho}\)), where \(\ell^\Phi_{\varphi,w}\) and \(\ell^\Psi_{\psi,\varrho}\) are two-weighted Orlicz sequence spaces, forms an algebra under pointwise multiplication whenever the weight sequences
\[
\varphi=\{\varphi_n\},\quad
\psi=\{\psi_n\},\quad
w=\{w_n\},\quad
\varrho=\{\varrho_n\}
\]
increase and satisfy the \(\Delta_2\)-condition.