2019
Том 71
№ 11

# Golubov B. I.

Articles: 2
Article (English)

### Fourier cosine and sine transforms and generalized Lipschitz classes in uniform metric

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 616-627

For functions $f \in L^1(\mathbb{R}_{+})$ with cosine (sine) Fourier transforms $\widehat{f}_c(\widehat{f}_s)$ in $L^1(\mathbb{R})$, we give necessary and sufficient conditions in terms of $\widehat{f}_c(\widehat{f}_s)$ for $f$ to belong to generalized Lipschitz classes $H^{\omega, m}$ and $h^{\omega, m}$. Conditions for the uniform convergence of the Fourier integral and for the existence of the Schwartz derivative are also obtained.

Article (Russian)

### On Modified Strong Dyadic Integral and Derivative

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 628-638

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 +).