On an Estimate of Calderón-zygmundoperators by Dyadic Positive Operators

A PROOF OF THE LOCAL Tb THEOREM FOR STANDARD CALDERÓN-ZYGMUND OPERATORS

We omit the proof. The following theorem is an extension of a local Tb Theorem for singular integrals introduced by M. Christ [Ch] in connection with the theory of analytic capacity. See also [NTV], where a non-doubling versions of Christ’s local Tb Theorem is given. A 1-dimensional version of the present result, valid for “perfect dyadic” Calder ón-Zygmund kernels, appears in [AHMTT]. In the s...

A Calderón-zygmund Estimate with Applications to Generalized Radon Transforms

We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators and generalized Radon transforms.

Multiscale Analysis for Ergodic Schrödinger Operators and Positivity of Lyapunov Exponents

A variant of multiscale analysis for ergodic Schrödinger operators is developed. This enables us to prove positivity of Lyapunov exponents given initial scale estimates and an initial Wegner estimate. This is then applied to high dimensional skew-shifts at small coupling, where initial conditions are checked using the Pastur–Figotin formalism. Furthermore, it is shown that for potentials genera...

A Note on Calderón-zygmund Singular Integral Convolution Operators

Maximal operator for pseudo-differential operators with homogeneous symbols

The aim of the present paper is to obtain a Sjölin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak L2 estimate for a maximal dyadic sum operato...