Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
23.01.1964
E-mail: Keywords: conjugate functions, singular integrals; $H^p$-spaces; bounded mean oscillation, bounded characteristic, functions with positive real part.
Subject:
For functions $f(z)$ in the Hardy class $H^p(0<p<\infty) $ it is known that $||f(re^{i\theta})-f(e^{i\theta})||_{L^p}<C_p\omega(1-r,f)_p$ where $\omega(\cdot,f)_p$ is the modulus of continuity of the boundary function $f(e^{i\theta})$. Extensions of this result are received to functions belonging to certain Hardy–Orlicz spaces. Proved that some resonance theorems for BMO and ReH are similar to the well-known Landau theorem in $L^p$-space.
Main publications:
Vartanyan G. M. Ob odnoi rezonansnoi teoreme // Izv. vuzov, 1990, 2, 3–13.
Vartanyan G. M. O skorosti priblizheniya funktsii iz klassov Khardi–Orlicha $H_\varphi$ // Matem. zametki, 1991, 50(5), 23–31.
Vartanyan G. M. Ob otsenke odnogo integrala na krivykh // Volinskii matematichnii visnik, 1996, 3, 31–34.
Dmitrishin D. V., Vartanyan G. M., Usov A. V. Absolyutnaya ustoichivost reguliruemykh sistem s posledeistviem // Trudy Odesskogo politekhn. un-ta. Nauchnyi i proizvodstvenno-prakticheskii sbornik po tekhnicheskim i estestvennym naukam, 2000, 2(11), 119–124.
Dmitrishin D. V., Vartanyan V. M., Vartanyan G. M. Kriterii ustoichivosti mekhanicheskikh sistem s uchetom zapazdyvaniya // Sb. nauchn. tr. Khark. Voen. un-t. Sistemy obrabotki informatsii, 2000, 3(9), 75–82.
