Multilinear proofs for two theorems on circular averages
For 1 ≤ p,q ≤ ∞, we prove that the convolution operator generated by the Cantor-Lebesgue measure on the circle is a contraction whenever it is bounded from to . We also give a condition on p which is necessary if this operator maps into L²().
We study L(R) → L (L ) estimates for the Radon transform in certain cases where the dimension of the measure μ on Σ is less than n-1.
Page 1