@inbook {7471, title = {Some algebras of functions with Fourier coefficients in weighted Orlicz sequence spaces}, booktitle = {Operator Theoretical Methods and Applications to Mathematical Physics. The Erhard Meister Memorial Volume. Operator Theory: Advances and Applications, 147}, year = {2004}, pages = {287-296}, publisher = {Birkh{\"a}user}, organization = {Birkh{\"a}user}, address = {Basel}, 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.

}, url = {http://link.springer.com/chapter/10.1007/978-3-0348-7926-2_31}, author = {Karlovich, Alexei Yu.}, editor = {Gohberg, Israel and Wendland, Wolfgang and Ferreira dos Santos, Ant{\'o}nio and Speck, Frank-Ollme and Teixeira, Francisco Sep{\'u}lveda} }