Open Access Research

On spectral properties of the modified convolution operator

Ainur Jumabayeva1,2*, Esmukhanbet Smailov3 and Nazerke Tleukhanova2

Author Affiliations

1 Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Barcelona, Bellaterra, 08193, Spain

2 Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Munaitpasova 5, Astana, 010008, Kazakhstan

3 Institute of Applied Mathematics, Gogolya 38, Karaganda, 470055, Kazakhstan

For all author emails, please log on.

Journal of Inequalities and Applications 2012, 2012:146 doi:10.1186/1029-242X-2012-146

Published: 25 June 2012

Abstract

We investigated the s-number of the modified convolution operator and obtained the following results

<a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M2">View MathML</a>, <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M3">View MathML</a>, G is a set of all segments Q from <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M4">View MathML</a>, F is a set of all compacts from <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M4">View MathML</a>, <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/146/mathml/M6">View MathML</a> is the measure of a set Q.

MSC: 42A45, 44A35.

Keywords:
Fourier series multipliers; convolution operator; s-number; Lorentz space; Besov space