Cobos, FernandoResina, Ivam2023-06-202023-06-201993COBOS, F.-On the Lorentz-Marcinkiewicz operator ideal, Math. Nachr., 126 (1986), 281-300. COBOS, F.-Entropy and Lorentz-Marcinkiewicz operator ideals, Arkiv Mat., 25 (1987), 211-219. COBOS, F. and KÜHN, T.-Entropy and eigenvalues of weakly singular integral operators, Integral Eq. and Operator Theory, 11 (1988), 64-86. KÖNING, H.-Weyl-type inequalities for operators in Banach spaces, in "Proc. Conf. Funct. Anal. Paderborn 1979", North Holland (1980), 297-317. MERUCCI, C.-Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces, in "Interpolation Spaces and Allied Topics in Analysis", Springer Lect. Notes Math., 1070 (1984), 183-201. PIETSCH, A.-Eigenvalues and s-Numbers, Cambridge Univ. Press, Cambridge (1987).0032-5155https://hdl.handle.net/20.500.14352/58675We show a direct proof for the generalized Hardy’s inequality obtained by the first author Math. Nachr. 126, 281-300, 1986. Our techniques are elementary and work in the limit case which was not covered in [loc. cit.]. Some applications to eigenvalue distributions of operator ideals are also given.engjournal articlehttp://purl.pt/3326/1/j-5293-b-vol50-fasc2-art3_PDF/j-5293-b-vol50-fasc2-art3_PDF_01-B-R0300/j-5293-b-vol50-fasc2-art3_0000_capa1-156_t01-B-R0300.pdfhttp://www.spm.pt/restricted access517.98Análisis funcional y teoría de operadores