Homogeneous kernels and self similar sets
Vasilis ChousionisMariusz Urbanski
32A5530L99Singular integralsself similar setsreal analyticitymetric spaces
We consider singular integrals associated with homogeneous kernels on self-similar sets. Using ideas from Ergodic Theory, we prove, among other things, that in Euclidean spaces the principal values of singular integrals associated with real analytic, homogeneous kernels fail to exist almost everywhere on self-similar sets satisfying some separation conditions. Furthermore, in general metric groups, using similar techniques, we generalize a criterion of $L^2$-unboundedness for singular integrals on self-similar sets.
Indiana University Mathematics Journal
2015
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10.1512/iumj.2015.64.5491
10.1512/iumj.2015.64.5491
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Indiana Univ. Math. J. 64 (2015) 411 - 431
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