Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

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Differential Transform of Cesàro averages in product spaces.

Cecilia Ferrari Freire

Universidad Nacional del Comahue - IITCI (CONICET), Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this poster we present convergence results for the series of differences of Cesàro averages along lacunary sequences in product spaces. These results give some information about how the Cesàro averages converge. From a result in [D] y [DRF] and following the ideas in [BMR] for the lacunar maximal operator in the lateral context we obtain new results in the product spaces context.

References

[BMR] Bernardis, A.L.; Mart\'\i n-Reyes, F.J.; \textit{Differential Transforms of Cesàro averages in weighted Spaces.} Publ. Math. 52 (2008), 101-127.

[D] Duoandikoetxea, J.; Multiple singular integrals and Maximal functions along hypersurfaces. Ann. Inst.Fourier, Grenoble. 36, 4(1986), 185-206.

[DRF] Duoandikoetxea, J. and Rubio de Francia, J.L.; Maximal and singular integral operators via Fourier transform estimates. Invent. Math. 84, 541-561 (1986).

Joint work with Raquel Crescimbeni (Universidad Nacional del Comahue - IITCI (CONICET), Argentina).

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