Source: Banach J. Math. Anal.
Volume 4, Number 1
We study new conditions on a radial function $f$ in order to have the almost
everywhere convergence of the spherical partial Fourier integrals.
Full-text: Access denied (no subscription
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157.
Mathematical Reviews (MathSciNet): MR199631
L. Colzani, A. Crespi, G. Travaglini and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in Euclidean and non-Euclidean spaces, Trans. Amer. Math. Soc. 338 (1993), 43–55
M. Carro and E. Prestini, Convergence a.e. of the spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates, Studia Math. 192 (2009), 173–194.
J. Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.
R. Hunt, On the convergence of Fourier series, Proc. Conf., Edwardsville, Ill. 1 (1967), 235–255.
Mathematical Reviews (MathSciNet): MR238019
B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226.
Mathematical Reviews (MathSciNet): MR293384
E. Prestini, Almost everywhere convergence of the spherical partial sums for radial functions, Monatsh. Math. 105 (1988), 207–216.
Mathematical Reviews (MathSciNet): MR939943
E. Romera, Weighted bounds for the Carleson maximal operator in $R\sp n$, Rend. Circ. Mat. Palermo (2)43 (1994), 98–106.
E. Romera and F. Soria, Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions, Monatsh. Math. 105 (1988), 207–216.
S. Yano, Notes on Fourier analysis. XXIX. An extrapolation theorem, J. Math. Soc. Japan 3 (1951), 296–305.
Mathematical Reviews (MathSciNet): MR48619