Mean and weak convergence of some orthogonal Fourier expansions by using Ap theory

  1. Guadalupe Hernández, José Javier
  2. Pérez, M.
  3. Varona Malumbres, Juan Luis
Revista:
Lecture Notes in Pure and Applied Mathematics

ISSN: 0075-8469

Año de publicación: 1989

Volumen: 117

Páginas: 161-169

Tipo: Artículo

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Otras publicaciones en: Lecture Notes in Pure and Applied Mathematics

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Resumen

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