On Modified Strong Dyadic Integral and Derivative

  • B. I. Golubov Moscow Inst. Phys. and Technol. (State Univ.), Russia


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 +).
How to Cite
Golubov, B. I. “On Modified Strong Dyadic Integral and Derivative”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 5, May 2002, pp. 628-3, https://umj.imath.kiev.ua/index.php/umj/article/view/4101.
Research articles