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    Embedding Relations Between Weighted Complementary Local Morrey-Type Spaces And Weighted Local Morrey-Type Spaces
    (L N Gumilyov Eurasian Natl Univ, 2017) Gogatishvili, A.; Mustafayev, R. Ch.; Unver, T.
    In this paper embedding relations between weighted complementary local Morreytype spaces (LMp theta,omega)-L-c(R-n, v) and weighted local Morrey-type spaces L LMp theta,omega(R-n, v) are characterized. In particular, two-sided estimates of the optimal constant c in the inequality (integral(infinity)(0) (integral(B(0,t)) f (x)(p2) v(2)(x)dx)(q2/p2) u(2)(t) dt)(1/q2) <= c (integral(infinity)(0)(integral(cB(0,t)) f (x)(p1) v(1)(x) dx)(q1/p1) u(1)(t) dt)(1/q1), f >= 0 are obtained, where p(1), p(2), q(1), q(2) is an element of (0, infinity), p(2) <= q(2) and u(1), u(2) and v(1), v(2) are weights on (0,infinity) and R-n, respectively. The proof is based on the combination of the duality techniques with estimates of optimal constants of the embedding relations between weighted local Morrey-type and complementary local Morrey-type spaces and weighted Lebesgue spaces, which allows to reduce the problem to using of the known Hardy-type inequalities.
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    NEW CHARACTERIZATION OF MORREY SPACES
    (L N Gumilyov Eurasian Natl Univ, 2013) Gogatishvili, A.; Mustafayev, R. Ch.
    In this paper we prove that the norm of the Morrey space Mp, lambda is equivalent to sup {integral R-n |fg| : inf(x is an element of R)(n) integral(infinity)(0) r(p)(n-lambda) -1
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    A Note on Boundedness of the Hardy-Littlewood Maximal Operator on Morrey Spaces
    (Springer Basel Ag, 2016) Gogatishvili, A.; Mustafayev, R. Ch
    In this paper we prove that the Hardy-Littlewood maximal operator is bounded on Morrey spaces M-1,M-lambda(R-n), 0 <= lambda < n for radial, non-increasing functions on R-n.
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    Some New Iterated Hardy-Type Inequalities
    (Hindawi Ltd, 2012) Gogatishvili, A.; Mustafayev, R. Ch; Persson, L-E
    We characterize the validity of the Hardy-type inequality parallel to parallel to integral(infinity)(s) h(z)dz parallel to(p,u,(0,t)) parallel to(q,w,(0,infinity)) <= c parallel to h parallel to(theta,v(0,infinity)), where 0 < p < infinity, 0 < q <= infinity, 1 < theta = infinity, u, w, and v are weight functions on (0,infinity). Some fairly new discretizing and antidiscretizing techniques of independent interest are used.