Best constants for two nonconvolution inequalities

Authors:
Michael Christ and Loukas Grafakos

Journal:
Proc. Amer. Math. Soc. **123** (1995), 1687-1693

MSC:
Primary 42B25; Secondary 26D15, 47B38

DOI:
https://doi.org/10.1090/S0002-9939-1995-1239796-6

MathSciNet review:
1239796

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Abstract: The norm of the operator which averages in over balls of radius centered at either 0 or *x* is obtained as a function of *n , p* and . Both inequalities proved are n-dimensional analogues of a classical inequality of Hardy in . Finally, a lower bound for the operator norm of the Hardy-Littlewood maximal function on is given.

**[BT]**Albert Baernstein II and B. A. Taylor,*Spherical rearrangements, subharmonic functions, and *-functions in 𝑛-space*, Duke Math. J.**43**(1976), no. 2, 245–268. MR**0402083****[HLP]**G. Hardy, J. Littlewood, and G. Pólya,*Inequalities*, The University Press, Cambridge, 1959.**[F]**William G. Faris,*Weak Lebesgue spaces and quantum mechanical binding*, Duke Math. J.**43**(1976), no. 2, 365–373. MR**0425598****[PS]**G. Pólya and G. Szegö,*Isoperimatric inequalities in mathematical physics*, Princeton Univ. Press, Princeton, NJ, 1951.**[S]**Elias M. Stein,*Singular integrals and differentiability properties of functions*, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR**0290095****[SO]**S. L. Sobolev,*On a theorem of functional analysis*, Mat. Sb. (N.S.)**4**(1938), 471-497; English transl., Amer. Math. Soc. Transl. Ser. 2, vol. 34, Amer. Math. Soc., Providence, RI, 1963, pp. 39-68.**[SS]**E. M. Stein and J.-O. Strömberg,*Behavior of maximal functions in 𝑅ⁿ for large 𝑛*, Ark. Mat.**21**(1983), no. 2, 259–269. MR**727348**, https://doi.org/10.1007/BF02384314**[SW]**Elias M. Stein and Guido Weiss,*Introduction to Fourier analysis on Euclidean spaces*, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR**0304972**

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1239796-6

Article copyright:
© Copyright 1995
American Mathematical Society