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    Embeddings Between Weighted Cesaro Function Spaces
    (ELEMENT, 2020) Unver, Tugce
    In this paper, we give the characterization of the embeddings between weighted Ces`aro function spaces. The proof is based on the duality technique, which reduces this problem to the characterizations of some direct and reverse Hardy-type inequalities and iterated Hardy-type inequalities.
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    Embeddings Between Weighted Copson And Cesaro Function Spaces
    (Springer Heidelberg, 2017) Gogatishvili, Amiran; Mustafayev, Rza; Unver, Tugce
    In this paper, characterizations of the embeddings between weighted Copson function spaces Cop(p1,q1)(u(1),v(1)) and weighted Cesaro function spaces Ces(p2,q2) (u(2) , v(2)) are given. In particular, two-sided estimates of the optimal constant c in the inequality (integral(infinity)(0) (integral(t)(0) f(tau)(p2)v2(tau)d tau)(q2/p2) u2(t)dt)(1/q2)& para;& para;<= c(integral(infinity)(0) (integral(t)infinity f(tau)(p1)v1(tau)d tau)(q1/p1) u1(t)dt)(1/q1), where p(1), p(2), q(1), q(2) is an element of (0,infinity), p(2) <= q(2) and u(1), u(2), v(1), v(2) are weights on (0,infinity) are obtained. The most innovative part consists of the fact that possibly different parameters p1 and p2 and possibly different inner weights v(1) and v(2) are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesaro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.
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    Öğe
    Pointwise multipliers between weighted copson and cesàro function spaces
    (Walter De Gruyter Gmbh, 2019) Gogatishvili, Amiran; Mustafayev, Rza Ch.; Unver, Tugce
    In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Cop(p1), (q1) ((u1,) (v1)) and weighted Cesaro function spaces Ces(p2, q2) (u(2), v(2)) is presented, where p(1), p(2), q(1), q(2) is an element of (0,infinity), p(2) <= q(2) and u(1), u(2), v(1), v(2) are weights on (0, infinity). (C) 2019 Mathematical Institute Slovak Academy of Sciences
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    Reverse Hardy-type inequalities for supremal operators with measures
    (Element, 2015) Mustafayev, Rza; Unver, Tugce
    In this paper we characterize the validity of the inequalities parallel to g parallel to(p,(a, b),lambda) <= c parallel to u(x)parallel to g parallel to(infinity,(x,b),mu) parallel to(q,(a,b),nu) and parallel to g parallel to(p,(a, b),lambda) <= c parallel to u(x)parallel to g parallel to(infinity,(a,x),mu) parallel to(q,(a,b),nu) for all non-negative Borel measurable functions g on the interval (a, b) subset of R, where 0 < p <= +infinity, 0 < q <= +infinity, lambda, mu and nu are non-negative Borel measures on (a, b), and u is a weight function on (a, b)