Almost everywhere convergence of the spherical partial sums for radial functions

On the capacity of sets of divergence associated with the spherical partial integral operator

“…n−1 ) and, so, S R (φG α )(x) → φG α (x) almost everywhere by [15], [20]. Thus, Lemma 5.4 is a stronger version of these result for φG α , but, when 0 < α ≤ n−1 2 , there is no such q.…”

“…, the localisation provided by Theorem 2 combined with the estimates established in [5,15,20,18] 2 -quasieverywhere on any region where g has either some smoothness or some appropriate symmetry (radiality, for example).…”

“…From Lemma 5.3 and some estimates in [20], it is a simple exercise to get the pointwise result alluded to above: …”

Almost Everywhere Convergence of Inverse Spherical Transforms on Noncompact Symmetric Spaces

“…In Section 1 the main tool will be the analogous result in the Euclidean spaces R n [11] which in turn is based on L s (R) estimates for Carleson operator against A s -weights, 1<s< .…”

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

“…Almost everywhere convergence of spherical partial Fourier integrals for radial functions in weighted spaces. In [25] one of the authors proved that if f is a radial function belonging to L p (R n ), 2n/(n + 1) < p < 2n/(n − 1), then S R f (x) converges a.e. to f (x) whenever R tends to ∞, where…”