Professor 

I am Raghad Shamsah , researcher in  harmonic analysis and some related fields (wavelets, Fourier series). Now I am working on some results related with your paper (on the almost every where convergence of wavelet summation methods). I stopped with the following questions.

 The maximal function operator of f in the Elies Stein paper (1976) which is bounded on L^P(R^ n), whenever p > n/(n - 1), and
n biger than or equal 3. Is it  stay pounded when we define the maximal function  on new space L^2(S^2)?

and
How can I define the maximal function operator when the function define on L^2(S^2) ?

I hope that  you  can answer on my questions.

thanks

Raghad Shamsah
MATHEMATICAL DEPARTMENT/INSPEM/ UNIVERSITY PUTRA MALAYSIA