Weighted Hardy inequalities, real interpolation methods and vector measures

Referencias bibliográficas

• Ariño, M.A., Muckenhoupt, B.: Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions. Trans. Am. Math. Soc. 320, 727–735 (1990)
• Bennett, C., Rudnick, K.: On Lorentz–Zygmund spaces. Dissertationes Math. (Rozprawy Mat.) 175 (1980)
• Bergh, J., Löfström, J.: Interpolation spaces. An introduction. Springer, Berlin (1976)
• Brudnyĭ, Y.A., Krugljak, Y.N.: Interpolation functors and interpolation spaces, vol. I. North-Holland Publishing Co., Amsterdam (1991)
• del Campo, R., Fernández, A., Manzano, A., Mayoral, F., Naranjo, F.: Interpolation with a parameter function and integrable function spaces with respect to vector measures. Math. Inequal. Appl. (to appear)
• del Campo, R., Fernández, A., Mayoral, F., Naranjo, F.: Complex interpolation of $$L^p$$ L p -spaces of vector measures on $$\delta $$ δ -rings. J. Math. Anal. Appl. 405, 518–529 (2013)
• del Campo, R., Fernández, A., Mayoral, F., Naranjo, F.: A note on real interpolation of $$L^p$$ L p -spaces of vector measures on $$\delta $$ δ -rings. J. Math. Anal. Appl. 419, 995–1003 (2014)
• Carro, M.J., Raposo, J.A., Soria, J.: Recent developments in the theory of Lorentz spaces and weighted inequalities. Mem. Amer. Math. Soc. 187, 877 (2007)
• Carro, M.J., Soria, J.: Weighted Lorentz spaces and the Hardy operator. J. Funct. Anal. 112, 480–494 (1993)
• Cerdà, J., Martín, J., Silvestre, P.: Capacitary function spaces. Collect. Math. 62, 95–118 (2011)
• Cwikel, M., Kamińska, A., Maligranda, L., Pick, L.: Are generalized Lorentz “spaces” really spaces? Proc. Am. Math. Soc. 132, 3615–3625 (2004)
• Diestel, J., Uhl Jr, J.J.: Vector measures. Mathematical Surveys, no. 15. American Mathematical Society, Providence (1977)
• Dobrakov, I.: On submeasures I. Dissertationes Math. (Rozprawy Mat.) 112 (1974)
• Fernández, A., Mayoral, F., Naranjo, F.: Real interpolation method on spaces of scalar integrable functions with respect to vector measures. J. Math. Anal. Appl. 376, 203–211 (2011)
• Fernández, A., Mayoral, F., Naranjo, F.: Bartle–Dunford–Schwartz integral versus Bochner, Pettis and Dunford integrals. J. Convex Anal. 20, 339–353 (2013)
• Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez-Pérez, E.A.: Spaces of $$p$$ p -integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)
• Fernández, A., Mayoral, F., Naranjo, F., Sánchez-Pérez, E.A.: Complex interpolation of spaces of integrable functions with respect to a vector measure. Collect. Math. 61(3), 241–252 (2010)
• Gustavsson, J.: A function parameter in connection with interpolation of Banach spaces. Math. Scand. 42, 289–305 (1978)
• Kalton, N.J., Peck, N.T., Roberts, J.W.: An $$F$$ F -space sampler. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1984)
• Klimkin, V.M., Svistula, M.G.: The Darboux property of a nonadditive set function. Sb. Math. 192, 969–978 (2001)
• Kluvánek, I., Knowles, G.: Vector measures and control systems. Notas de Matemática, no. 58, North-Holland, Amsterdam (1976)
• Okada, S., Ricker, W.J., Sánchez-Pérez, E.A.: Optimal domain and integral extension of operators: acting in function spaces. Operator theory: advances and applications. Birkhäuser, Basel (2008)
• Persson, L.E.: Interpolation with a parameter function. Math. Scand. 59, 199–222 (1986)
• Sawyer, E.: Boundedness of classical operators on classical Lorentz spaces. Studia Math. 96, 145–158 (1990)