IST IST

Seminar on
Functional Analysis and Applications

Supported by The Centre for Mathematics and its Applications - CEMAT
and FCT project POCTI/34222/MAT/2000. 


      

        



	


        
    
          
  • September 17, 2004, Friday - 15h15 (Room P 3.10): 
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Boundary Value Problems for
Analytic Functions and Singular Operators in the Variable Exponent
Spaces with General Weights
        

        

        Stefan Samko

        
 

        

        
(Universidade do Algarve, Faro)

        



         
 Abstract.  We consider the Riemann boundary value 
problem
for analytic functions in the class of analytic functions represented
by the Cauchy type integral with density in the generalized Lebesgue
spaces with variable exponent. We consider both the cases when the
coefficient  G  is  piecewise continuous  or it may be of a more
general nature, admitting its oscillation. The solvability conditions
are derived and in all the cases of solvability the explicit formulas
are given. Following the approach of I.Simonenko, we make use of the
results on the explicit solution  of the boundary value problem  to
obtain the weight results for Cauchy singular integral operator in
Lebesgue spaces with variable exponent, among them some extension of
the well known Helson-Szego theorem.



	



        

        
Seminars take place in Lisbon, I.S.T. - 
Post Graduation Building

Webpage: http://www.math.ist.utl.pt/funcional