On W1,p,p-convergence of Fourier&-Sobolev expansions Articles uri icon

publication date

  • February 2013

issue

  • 2

volume

  • 398

international standard serial number (ISSN)

  • 0022-247X

electronic international standard serial number (EISSN)

  • 1096-0813

abstract

  • Let {qn}n0 be the sequence of polynomials orthonormal with respect to the Sobolev inner product ⟨f,g⟩S:=∫1−1f(x)g(x)w0(x)dx+∫1−1f′(x)g′(x)w1(x)dx,Turn MathJax off where w0∈L∞([−1,1]) and w1 is a weight of Kufner&-Opic type. We study necessary and/or sufficient conditions for the convergence in the W1,p([−1,1],(w0,w1)) norm of the Fourier expansion in terms of {qn}n≥0, with 1