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Weak type (1, 1) inequalities of maximal convolution operators

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Abstract

In this paper we study the behavior of the constants which appear in the weak type (1, 1) inequalities for maximal convolution operators by means of discrete methods.

One of the first applications of these techniques will give us a very simple proof of the ergodic theorem. We also present partial results in order to investigate the best constant in the weak type (1, 1) inequality for the Hardy-Littlewood centered maximal operator in dimension one. In dimension bigger than one we also obtain some lower bounds for that constant.

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Authors and Affiliations

  1. Dept. de Matematicas, C-XVI, Universidad Autonoma de Madrid, 28049, Madrid, Spain

    M. Trinidad Menarguez & Fernando Soria

Authors
  1. M. Trinidad Menarguez
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  2. Fernando Soria
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Partially supported by D.G.I.C.Y.T.

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Menarguez, M.T., Soria, F. Weak type (1, 1) inequalities of maximal convolution operators. Rend. Circ. Mat. Palermo 41, 342–352 (1992). https://doi.org/10.1007/BF02848939

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  • DOI: https://doi.org/10.1007/BF02848939

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