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Abstract In this article, we analyze the boundedness for the fractional bilinear Hardy operators on variable exponent weighted Morrey–Herz spaces M K ˙ q , p ( ⋅ ) α ( ⋅ ) , λ ( w ) ${M\dot{K}^{\alpha (\cdot ),\lambda}_{q,p(\cdot)}(w)}$ . Similar estimates are obtained for their commutators when the symbol functions belong to BMO space with variable exponents.

Abstract The present article discusses the boundedness criteria for the fractional Hardy operators on weighted variable exponent Morrey–Herz spaces M K ˙ q , p ( ⋅ ) α ( ⋅ ) , λ ( w ) ${M\dot{K}^{\alpha(\cdot),\lambda}_{q,p(\cdot)}(w)}$ .

Abstract In this paper, we discuss some new Hilbert-type dynamic inequalities on time scales in two separate variables. We also deduce special cases, like some integral and their respective discrete inequalities.

Abstract The aim of this paper is to prove the boundedness of the oscillation and variation operators for the multilinear singular integrals with Lipschitz functions on weighted Morrey spaces.

Abstract In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α $I_{\alpha}$ in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ b , I α ] $[b,I_{\alpha}]$ formed by b and I α $I_{\alpha}$ are established. Also we study related problems about two-weight, weak type inequalities for I α $I_{\alpha}$ and [ b , I α ] $[b,I_{\alpha}]$ in the Morrey-type spaces and give partial results.

For a wide class of weights, a systematic investigation of the convergence-divergence behavior of Lagrange interpolation is initiated. A system of nodes with optimal Lebesgue constant is found, and for Hermite weights an exact lower estimate of the norm of projection operators isgiven. In the same spirit, the case of Hermite–Fejér interpolation is also considered.

Abstract In this article, we characterize the pairs (u, v) of positive measurable functions such that T maps the weighted amalgam in (Lp (u), ℓ q ) for all , where T belongs to a class of positive operators which includes Hardy operators, maximal operators, and fractional integrals. 2000 Mathematics Subject Classification 26D10, 26D15 (42B35)

We construct rational operators for the weighted uniform approximation on the semiaxis. Direct and converse results are shown which are not possible for polynomials.

For a wide class of weights, a systematic investigation of the convergence-divergence behavior of Lagrange interpolation is initiated. A system of nodes with optimal Lebesgue constant is found, and for Hermite weights an exact lower estimate of the norm of projection operators isgiven. In the same spirit, the case of Hermite–Fejér interpolation is also considered.