Mean and weak convergence of some orthogonal Fourier expansions by using Ap theory
ISSN: 0075-8469
Any de publicació: 1989
Volum: 117
Pàgines: 161-169
Tipus: Article
Altres publicacions en: Lecture Notes in Pure and Applied Mathematics
Resum
Lp convergence of Fourier expansions in orthogonal polynomials is studied for general (but around the endpoints Jacobi-like) weights of orthogonality. The authors observe that the problem is related to Muckenhoupt's Ap conditions. A sufficient condition is verified for norm convergence; however, the condition involves the orthogonal polynomials as well, not just the weights. It is also shown that a necessary condition for norm convergence proved by A. Máté, P. Nevai and the reviewer is actually necessary for the weak boundedness of the partial sums