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  • Küçük Resim
    Öğe
    Generalized Fractional Maximal Functions In Lorentz Spaces Λ
    (Element, 2018) Mustafayev, R. Ch; Bilgicli, N.
    In this paper we give the complete characterization of the boundedness of generalized fractional maximal operator M-phi,Lambda(alpha)(b)f(x):=Sup(Q(sic)x) parallel to f chi Q parallel to(Lambda alpha(b))/phi(vertical bar Q vertical bar) (x is an element of R-n), between the classical Lorentz spaces Lambda(P)(v) and Lambda(q)(w), as well as between Lambda(P)(v) and weaktype Lorentz spaces Lambda(q)(,infinity)(w), and between Lambda(P,infinity)(v) and Lambda(q,infinity)(w), and between Lambda(P,infinity)(v) and Lambda(q)(w), for appropriate functions phi, where 0 < p, q,alpha < infinity, v,w, b are weights on (0, infinity) such that 0 < B(t) := integral(t)(0) b infinity, t 0, B is an element of Delta(2) and B(t)/t(r) is quasi-increasing for some 0 < r <= 1.
  • Küçük Resim
    Öğe
    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.