Spherical summation: a problem of E.M. Stein
Annales de l'Institut Fourier, Volume 31 (1981) no. 3, p. 147-152
Writing (T R λ f) ^(ξ)=(1-|ξ| 2 /R 2 ) + λ f ^(ξ). E. Stein conjecturedj|TRjλfi|21/2pCj|fj|21/2pfor λ>0, 4 3p4 and C=C λ,p . We prove this conjecture. We prove also f(x)=lim j T 2 j λ f(x) a.e. We only assume 4 3+2λ<p<4 1-2λ.
Écrivons (T R λ f) ^(ξ)=(1-|ξ| 2 /R 2 ) + λ f ^(ξ). E. Stein a supposé quej|TRjλfi|21/2pCj|fj|21/2ppour λ>0, 4 3p4 et C=C λ,p . Nous démontrons cette conjecture. Nous démontrons aussi f(x)=lim j T 2 j λ f(x) presque partout. Nous supposons seulement 4 3+2λ<p<4 1-2λ.
@article{AIF_1981__31_3_147_0,
     author = {Cordoba, Antonio and Lopez-Melero, B.},
     title = {Spherical summation: a problem of E.M. Stein},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {31},
     number = {3},
     year = {1981},
     pages = {147-152},
     doi = {10.5802/aif.842},
     mrnumber = {83g:42008},
     zbl = {0464.42006},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1981__31_3_147_0}
}
Cordoba, Antonio; Lopez-Melero, B. Spherical summation: a problem of E.M. Stein. Annales de l'Institut Fourier, Volume 31 (1981) no. 3, pp. 147-152. doi : 10.5802/aif.842. https://aif.centre-mersenne.org/item/AIF_1981__31_3_147_0/

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