engleski

Improving estimates for discrete polynomial averaging operators

It as a well-known property of all averaging-type operators that their operator norms are at most $1$, simply as a consequence of the triangle inequality. In general, constant 1 cannot be improved, even when one considers various $L^p\to L^q$ estimates for $p\neq q$. However, certain averaging operators allow a significant improvement of this constant, which finds applications to various problems in the harmonic analysis. Here we study averaging operators in a discrete polynomial setting, and prove sharp improving $l^p\to l^q$ estimates in a close-to-optimal range of exponents (p, q). This is joint work with R. Han, M. T. Lacey, F. Yang (Georgia Institute of Technology), and J. Madrid (University of California, Los Angeles).

improving estimate, discrete average, polynomial

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