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Showing 1 to 4 of 4 for “"Besicovitch"”.
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Qualitative and Quantitative Analysis of Weighted Ergodic Theorems
… validity of the weighted ergodic theorem with Besicovitch weights. This, again, was known to hold in the duality range; however, we prove here that the result fails for each pair of nondual indices. The positive results we obtain are about stationary sequences with finite first moment. In this …
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Linear and multilinear spherical maximal functions
… versions of the Kakeya, Nikodym, and Besicovitch constructions associated with a fixed rectifiable set. These yield counterexamples indicating that maximal operators given by translations of spherical averages are unbounded on all Lp(Rn) for p [less than] [infinity]. For …
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Estimating the Hausdorff dimension
… the knowledge of the fractal, or Hausdorff-Besicovitch, dimension. However, no statistical properties of the usual estimator, the entropy estimator, are known. In addition, the entropy estimator is biased high when an inefficient net is used. This dissertation develops a new estimator, the …