On 11.05.2016, at 10:00 a.m. the next weekly seminar will be held dos. M.G.Gadjibekov, senior research fellow of the department ” Mathematical analysis”, will deliver a speech on the topic entitled “Generalized potentials on spaces with variable exponent”.
In the report we will consider generalized potential operators with the kernel ([p(x;y)])/[p(x,y)]N on bounded quasimetric measure space (X, ρ, μ) with doubling measure μ satisfying the upper growth condition μB(x,r) ≤ KrN , N ⊄ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we will discuss problems of the boundedness of these potential operators from the variable exponent Lebesgue space  Lp(•)(X, μ) into a certain Musielak-Orlicz space LΦ(X, μ) with the N-function Φ(x,r) defined by the exponent p(x) and the function a(r).