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Apr 22, 2016 at 1:15 history edited Mark Lewko CC BY-SA 3.0
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Apr 22, 2016 at 0:50 history edited Mark Lewko CC BY-SA 3.0
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Apr 21, 2016 at 19:23 comment added Todd Trimble @TerryTao (and/or Mark Lewko): do you have a good idea which paper(s) the OP is referring to (in the versions of the question before the edit by Leitão)? I suppose an answer to that would also answer the question of whom he is addressing.
Apr 21, 2016 at 17:42 comment added Terry Tao It may be that the OP is interested in "variable coefficient" versions of these theorems suitable for curved manifolds such as $S^2$. In this case one can look at Chapter XI.3 of Stein's "Harmonic analysis", which basically shows that the results of Stein extend to variable coefficient settings so long as a "rotational curvature" condition is satisfied. In 2D one needs a "cinematic curvature" condition; see Chapter XI.4.D of Stein.
Apr 21, 2016 at 17:33 history edited Terry Tao CC BY-SA 3.0
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Apr 21, 2016 at 12:07 history answered Mark Lewko CC BY-SA 3.0