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    Boundedness of operators arising from Schwarz BVP in modified local Morrey-type spaces
    (Taylor & Francis Ltd, 2017) Guliyev, V. S.; Koca, K.; Mustafayev, R. C. H.; Unver, T.
    In this paper, we prove the boundedness of a class of operators arising from Schwarz BVP in modified local Morrey-type spaces in the unit disc of the complex plane.
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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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    Embeddings between weighted local Morrey-type spaces and weighted Lebesgue spaces
    (Element, 2015) Mustafayev, R. Ch.; Unver, T.
    In this paper, the embeddings between weighted localMorrey-type spaces and weighted Lebesgue spaces are investigated.
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    Multidimensional Bilinear Hardy Inequalities
    (INST MATH & MECHANICS AZERBAIJAN, 2020) Bilgicli, N.; Mustafayev, R. Ch; Unver, T.
    Our goal in this paper is to find a characterization of n-dimensional bilinear Hardy inequalities parallel to integral(B(0,.)) f.integral(B(0,.)) g parallel to(q,u(0,infinity) )<= C parallel to f parallel to(p1,v1,Rn)parallel to g parallel to(p2,v2,Rn), f, g is an element of M+(R-n), parallel to integral c(B(0,.)) f.integral c(B(0,.)) g parallel to(q,u(0,infinity) )<= C parallel to f parallel to(p1,v1,Rn)parallel to g parallel to(p2,v2,Rn), f, g is an element of M+(R-n), when 0 < q <= infinity, 1 <= p1, p2 <= infinity and u and v1, v 2 are weight functions on (0,infinity ) and , R-n, respectively. Obtained results are new when p(i) = 1 or p(i) =infinity, i = 1, 2, or 0 < q <= 1 even in 1-dimensional case. Since the solution of the first inequality can be obtained from the characterization of the second one by usual change of variables we concentrate our attention on characterization of the latter. The characterization of this inequality is easily obtained for p(1) <= q using the characterizations of multidimensional weighted Hardy-type inequalities while in the case q < p(1) the problem is reduced to the solution of multidimensional weighted iterated Hardy-type inequality. To achieve our goal, we characterize the validity of multidimensional weighted iterated Hardy-type inequality parallel to parallel to integral cB((0,s)) h(z)dz parallel to(p,u,(0,t))parallel to(q,mu,(0,infinity) <= c parallel to h parallel to(theta,v,(0,infinity),) h is an element of M+(R-n) where 0 < p, q < infinity, 1 <= theta <= infinity, u is an element of W (0, infinity ), v is an element of W(R-n) and mu is a non-negative Borel measure on (0, infinity). We are able to obtain the characterization under the additional condition that the measure mu is non-degenerate with respect to U-q/p.
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    Some Operators Arising From Schwarz Bvp In Complementary Local Morrey-Type Spaces On The Unit Disc
    (Univ Prishtines, 2017) Guliyev, V. S.; Koca, K.; Mustafayev, R. Ch.; Unver, T.
    In this paper, we prove the boundedness of a class of operators arising from Schwarz BVP in complementary local Morrey-type spaces in the unit disc of the complex plane.