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- W561471102 abstract "We characterize the validity of the bilinear Hardy inequality for nonincreasing functions [ |f^{**} g^{**}|_{L^q(w)} le C |f|_{Lambda^{p_1}(v_1)}|g|_{Lambda^{p_2}(v_2)}, ] in terms of the weights $v_1$, $v_2$, $w$, covering the complete range of exponents $p_1,p_2,qin (0,infty]$. The problem is solved by reducing it into the iterated Hardy-type inequalities begin{align*} left( intlimits_0^infty biggl( intlimits_0^x (g^{**}(t))^alpha varphi(t),mathrm{d}t biggr)^frac{beta}{alpha} psi(x),mathrm{d}x right)^frac{1}{beta} & le C biggl( intlimits_0^infty (g^*(x))^gamma omega(x) ,mathrm{d}x biggr)^frac{1}{gamma}, left( intlimits_0^infty biggl( intlimits_x^infty (g^{**}(t))^alpha varphi(t),mathrm{d}t biggr)^frac{beta}{alpha} psi(x),mathrm{d}x right)^frac{1}{beta} & le C biggl( intlimits_0^infty (g^*(x))^gamma omega(x) ,mathrm{d}x biggr)^frac{1}{gamma}. end{align*} Validity of these inequalities is characterized here for $0ltalphalebetaltinfty$ and $0ltgammaltinfty$." @default.
- W561471102 created "2016-06-24" @default.
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- W561471102 date "2017-01-01" @default.
- W561471102 modified "2023-10-16" @default.
- W561471102 title "Bilinear weighted Hardy inequality for nonincreasing functions" @default.
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- W561471102 doi "https://doi.org/10.5565/publmat_61117_01" @default.
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