2017
Том 69
№ 9

All Issues

On Modified Strong Dyadic Integral and Derivative

Golubov B. I.

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Abstract

For functions fL(R +), we define a modified strong dyadic integral J(f) ∈ L(R +) and a modified strong dyadic derivative D(f) ∈ L(R +). We establish a necessary and sufficient condition for the existence of the modified strong dyadic integral J(f). Under the condition \(\smallint _{R_ + }\) f(x)dx = 0, we prove the equalities J(D(f)) = f and D(J(f)) = f. We find a countable set of eigenfunctions of the operators J and D. We prove that the linear span L of this set is dense in the dyadic Hardy space H(R +). For the functions fH(R +), we define a modified uniform dyadic integral J(f) ∈ L (R +).

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 5, pp 770-784.

Citation Example: Golubov B. I. On Modified Strong Dyadic Integral and Derivative // Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 628-638.

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