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Keywords:
maximal functions; spaces of homogeneous type
maximal functions; spaces of homogeneous type
Summary:
Given a rotation invariant measure in $\Bbb R^n$, we define the maximal operator over circular sectors. We prove that it is of strong type $(p,p)$ for $p>1$ and we give necessary and sufficient conditions on the measure for the weak type $(1,1)$ inequality. Actually we work in a more general setting containing the above and other situations.
References:
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[3] Pólya G., Szegö G.: Problems and Theorems in Analysis. Volume I, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
[4] de Guzmán M.: Real Variable Methods in Fourier Analysis. North Holland, Amsterdam, 1981. MR 0596037
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[6] Aimar H., Harboure E., Iaffei B.: Extensions of a theorem of Stein and Zygmund. preprint.
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