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Improved bounds for Stein's square functions
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Improved bounds for Stein's square functions
classification
math.CA
math.AP
keywords
boundsassociatedbochner--rieszclassesequationsfourierfunctionsimproved
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We prove a weighted norm inequality for the maximal Bochner--Riesz operator and the associated square-function. This yields new $L^p(R^d)$ bounds on classes of radial Fourier multipliers for $p\ge 2+4/d$ with $d\ge 2$, as well as space-time regularity results for the wave and Schr\"odinger equations.
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