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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

Citations:

Zbl 0910.42014
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