Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions

Romera, Elena; Soria, Fernando

doi:10.1090/S0002-9939-1991-1068130-6

Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions
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by Elena Romera and Fernando Soria PDF

Proc. Amer. Math. Soc. 111 (1991), 1015-1022 Request permission

Abstract:

Let $Tf(x) = {\sup _{R > 0}}\left | {{S_R}f(x)} \right |$ where ${S_R}$ is the spherical partial sum operator. We show that $T$ is bounded from the Lorentz space ${L_{{p_i},1}}({{\mathbf {R}}^n})$ into ${L_{{p_i},\infty }}({{\mathbf {R}}^n}),i = 0,1$ when acting on radial functions and where ${p_0} = \tfrac {{2n}}{{n + 1}},{p_1} = \tfrac {{2n}}{{n - 1}}$.

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