## The two-parameter operators.(English)Zbl 0929.42017

Summary: In the one-dimensional case is already proved [T. Eisner, Acta Sci. Math. 64, No 1-2, 201-214 (1998; Zbl 0910.42014)] that the dyadic Cesàro operator is bounded on $$L^p[0,1)$$ $$(1\leq p<\infty)$$ and on the dyadic Hardy space $$H^1[0,1)$$ and is not bounded on the spaces VMO and on $$L^\infty [0,1)$$. In the present paper we show similar results in the two-dimensional case.

### MSC:

 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42B30 $$H^p$$-spaces

Zbl 0910.42014
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