The Institute seminar on “Generalized potentials in variable exponent spaces” was held.
Today at the Institute seminar, senior research associate of “Mathematical Analysis” department of IMM M.G. Gadjibekov gave a talk on “Generalized potentials in variable exponent spaces”.

The talk deals with 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 the 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).

Previous Next