Some maximal lnequalities with respect to two-parameter dyadic derivative and cesàro summability

Abstract

We consider two-dimensional convolution operators with general kernel functions and give a sufficient condition for the two-parameter maximal operator to be bounded from the dyadic martingale Hardy space H_p to L_p. Especially, the boundedness of the maximal operator of the twoparameter dyadic derivative of the dyadic integral function and the maximal operator of the two-parameter Cesàro means are verified. As a consequence we obtain that every function f ∊ L log+ L[O, 1)² is Cesho summable and the dyadic integral of it is dyadically differentiable.

Keywords:

• martingale hardy spaces
• rectangle atoms
• quasi-local operators
• interpolation
• walsh function
• dyadic derivative
• cesàro summability

Additional information

Notes on contributors

Ferenc Weisz