Abstract
In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Copp1,q1(u1, v1) and weighted Cesàro function spaces Cesp2,q2(u2, v2) is presented, where p1, p2, q1, q2 ∈ (0, ∞), p2 ≤ q2 and u1, u2, v1, v2 are weights on (0, ∞).
Communicated by Marcus Waurick
Acknowledgement
We thank the anonymous referee for his / her remarks, which have improved the final version of this paper.
References
[1] Askey, R.—Boas, R. P., Jr.: Some integrability theorems for power series with positive coefficients. In: Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, pp. 23–32.Search in Google Scholar
[2] Astashkin, S. V.—Maligranda, L.: Structure of Cesàro function spaces, Indag. Math. (N.S.) 20(3) (2009), 329–379.10.1016/S0019-3577(10)00002-9Search in Google Scholar
[3] Astashkin, S. V.—Maligranda, L.: Structure of Cesàro function spaces: a survey, Banach Center Publ. 102 (2014), 13–40.10.4064/bc102-0-1Search in Google Scholar
[4] Bennett, G.: Factorizing the Classical Inequalities. Mem. Amer. Math. Soc. 120, 1996.10.1090/memo/0576Search in Google Scholar
[5] Boas, R. P., Jr.: Integrability Theorems for Trigonometric Transforms. Ergeb. Math. Grenzgeb. (3) 38, Springer-Verlag New York Inc., New York, 1967.10.1007/978-3-642-87108-5_1Search in Google Scholar
[6] Boas, R. P., Jr.: Some integral inequalities related to Hardy’s inequality, J. Analyse Math. 23 (1970), 53–63.10.1007/BF02795488Search in Google Scholar
[7] Gogatishvili, A.—Kufner, A.—Persson, L.-E.: Some new scales of weight characterizations of the classBp, Acta Math. Hungar. 123 (2009), 365–377.10.1007/s10474-009-8132-zSearch in Google Scholar
[8] Gogatishvili, A.—Mustafayev, R. Ch.—Ünver, T.: Embeddings between weighted Copson and Cesàro function spaces, Czechoslovak Math. J. 67 (2017), 1105–1132.10.21136/CMJ.2017.0424-16Search in Google Scholar
[9] Gogatishvili, A.—Persson, L.-E.—Stepanov, V. D.—Wall, P.: Some scales of equivalent conditions to characterize the Stieltjes inequality: the caseq < p, Math. Nachr. 287 (2014), 242–253.10.1002/mana.201200118Search in Google Scholar
[10] Gogatishvili, A.—Pick, L.: Discretization and anti-discretization of rearrangement-invariant norms, Publ. Mat. 47 (2003), 311–358.10.5565/PUBLMAT_47203_02Search in Google Scholar
[11] Gogatishvili, A.—Pick, L.: Embeddings and duality theorems for weak classical Lorentz spaces, Canad. Math. Bull. 49 (2006), 82–95.10.4153/CMB-2006-008-3Search in Google Scholar
[12] Goldman, M. L.—Heinig, H. P.—Stepanov, V. D.: On the principle of duality in Lorentz spaces, Canad. J. Math. 48 (1996), 959–979.10.4153/CJM-1996-050-3Search in Google Scholar
[13] Grosse-Erdmann, K.-G.: The blocking technique, weighted mean operators and Hardy’s inequality. Lecture Notes in Math. 1679, Springer-Verlag, Berlin, 1998.Search in Google Scholar
[14] Jagers, A. A.: A note on Cesàro sequence spaces, Nieuw Arch. Wisk. (3) 22 (1974), 113–124.Search in Google Scholar
[15] Kamińska, A.—Kubiak, D.: On the dual of Cesàro function space, Nonlinear Anal. 75 (2012), 2760–2773.10.1016/j.na.2011.11.019Search in Google Scholar
[16] Kolwicz, P.—Leśnik, K.—Maligranda, L.: Pointwise multipliers of Calderón-Lozanovskiĭ spaces, Math. Nachr. 286 (2013), 876–907.10.1002/mana.201100156Search in Google Scholar
[17] Kolwicz, P.—Leśnik, K.—Maligranda, L.: Symmetrization, factorization and arithmetic of quasi-Banach function spaces, J. Math. Anal. Appl. 470 (2019), 1136–1166.10.1016/j.jmaa.2018.10.054Search in Google Scholar
[18] Leibowitz, G. M.: A note on the Cesàro sequence spaces, Tamkang J. Math. 2 (1971), 151–157.Search in Google Scholar
[19] Programma van Jaarlijkse Prijsvragen (Annual Problem Section). Nieuw Arch. Wiskd. 16 (1968), 47–51.Search in Google Scholar
[20] Shiue, J.-S.: A note on Cesàro function space, Tamkang J. Math. 1 (1970), 91–95.Search in Google Scholar
[21] Sy, P. W.—Zhang, W. Y.—Lee, P. Y.: The dual of Cesàro function spaces, Glas. Mat. Ser. III, 22 (1987), 103–112.Search in Google Scholar
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