References
- I. Al Alam, L. Gaillard, G. Habib, P. Lefevre, and F. Maalouf, Essential norm of Cesaro operators on Lp and Cesaro spaces, J. Math. Anal. Appl. 467 (2018), no. 2, 1038-1065. https://doi.org/10.1016/j.jmaa.2018.07.038
- S. V. Astashkin and L. Maligranda, Cesaro function spaces fail the fixed point property, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4289-4294. https://doi.org/10.1090/S0002-9939-08-09599-3
- S. V. Astashkin and L. Maligranda, Structure of Cesaro function spaces, Indag. Math. (N.S.) 20 (2009), no. 3, 329-379. https://doi.org/10.1016/S0019-3577(10)00002-9
- S. V. Astashkin and L. Maligranda, Rademacher functions in Cesaro type spaces, Studia Math. 198 (2010), no. 3, 235-247. https://doi.org/10.4064/sm198-3-3
- S. V. Astashkin and L. Maligranda, Geometry of Cesaro function spaces, Funktsional. Anal. i Prilozhen. 45 (2011), no. 1, 79-83; English transl.: Funct. Anal. Appl. 45 (2011), 64-68.
- S. V. Astashkin and L. Maligranda, Interpolation of Cesaro sequence and function spaces, Studia Math. 215 (2013), no. 1, 39-69. https://doi.org/10.4064/sm215-1-4
- S. V. Astashkin and L. Maligranda, A short proof of some recent results related to Cesaro function spaces, Indag. Math. (N.S.) 24 (2013), no. 3, 589-592. https://doi.org/10.1016/j.indag.2013.03.001
- S. V. Astashkin and L. Maligranda, Interpolation of Cesaro and Copson spaces, in: Banach and Function Spaces IV (Kitakyushu, 2012), Yokohama Publ., Yokohama 2014, 123-133.
- N. L. Braha, Structure of Cesaro second order function spaces, Miskolc Math. Notes 16 (2015), no. 2, 705-711. https://doi.org/10.18514/MMN.2015.1385
- P. Butzer and C. Bardaro, Mellin analysis and exponential sampling. Part I: Mellin fractional integrals, Proceedings of the 10th International Conference on Sampling Theory and Applications, 274-276.
- P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl. 269 (2002), no. 1, 1-27. https://doi.org/10.1016/S0022-247X(02)00001-X
- P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl. 269 (2002), no. 2, 387-400. https://doi.org/10.1016/S0022-247X(02)00049-5
- P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl. 270 (2002), no. 1, 1-15. https://doi.org/10.1016/S0022-247X(02)00066-5
- G. P. Curbera and W. J. Ricker, Abstract Cesaro spaces: integral representations, J. Math. Anal. Appl. 441 (2016), no. 1, 25-44. https://doi.org/10.1016/j.jmaa.2016.03.074
- G. B. Folland, Real Analysis: modern techniques and their applications, John Wiley & Sons, 1984.
- A. Gogatishvili, R. Mustafayev, and T. Unver, Embeddings between weighted Copson and Cesaro function spaces, Czechoslovak Math. J. 67(142) (2017), no. 4, 1105-1132. https://doi.org/10.21136/CMJ.2017.0424-16
- A. Gogatishvili, R. Mustafayev, and T. Unver, Pointwise multipliers between weighted Copson and Cesaro function spaces, Math. Slovaca 69 (2019), no. 6, 1303-1328. https://doi.org/10.1515/ms-2017-0310
- R. Herrmann, Towards a geometric interpretation of generalized fractional integrals-Erdelyi-Kober type integrals on RN , as an example, Fract. Calc. Appl. Anal. 17 (2014), no. 2, 361-370. https://doi.org/10.2478/s13540-014-0174-4
- K.-P. Ho, Integral operators on BMO and Campanato spaces, Indag. Math. (N.S.) 30 (2019), no. 6, 1023-1035. https://doi.org/10.1016/j.indag.2019.05.007
- K.-P. Ho, Erdelyi-Kober fractional integrals on Hardy space and BMO, Proyecciones 39 (2020), no. 3, 663-677. https://doi.org/10.22199/issn.0717-6279-2020-03-0041
- K.-P. Ho, Erdelyi-Kober fractional integral operators on ball Banach function spaces, Rend. Semin. Mat. Univ. Padova 145 (2021), 93-106. https://doi.org/10.4171/rsmup/72
- K.-P. Ho, Hardy's inequalities and Erdelyi-Kober fractional integrals on BMO(ρ), Azerb. J. Math. 11 (2021), no. 1, 92-103.
- K.-P. Ho, Hardy's inequalities, Hilbert inequalities and fractional integrals on function spaces of q-integral p-variation, Ann. Polon. Math. 126 (2021), no. 3, 251-263. https://doi.org/10.4064/ap200224-11-1
- M. Ilkhan, S. Demiriz, and E. E. Kara, Multiplication operators on Cesaro second order function spaces, Positivity 24 (2020), no. 3, 605-614. https://doi.org/10.1007/s11117-019-00700-5
- V. Kiryakova, Generalized fractional calculus and applications, Pitman Research Notes in Mathematics Series, 301, Longman Scientific & Technical, Harlow, 1994.
- V. Kiryakova, Transmutation method for solving hyper-Bessel differential equations based on the Poisson-Dimovski transformation, Fract. Calc. Appl. Anal. 11 (2008), no. 3, 299-316.
- T. Kiwerski and P. Kolwicz, Rotundity and monotonicity properties of selected Cesaro function spaces, Positivity 22 (2018), no. 1, 357-377. https://doi.org/10.1007/s11117-017-0515-8
- A. Kufner, L. Maligranda, and L.-E. Persson, The prehistory of the Hardy inequality, Amer. Math. Monthly 113 (2006), no. 8, 715-732. https://doi.org/10.2307/27642033
- A. Kufner, L.-E. Persson, and N. Samko, Weighted Inequalities of Hardy Type, second edition, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017. https://doi.org/10.1142/10052
- K. Lesnik and L. Maligranda, Abstract Cesaro spaces. Duality, J. Math. Anal. Appl. 424 (2015), no. 2, 932-951. https://doi.org/10.1016/j.jmaa.2014.11.023
- K. Lesnik and L. Maligranda, Abstract Cesaro spaces. Optimal range, Integral Equations Operator Theory 81 (2015), no. 2, 227-235. https://doi.org/10.1007/s00020-014-2203-4
- K. Lesnik and L. Maligranda, Interpolation of abstract Cesaro, Copson and Tandori spaces, Indag. Math. (N.S.) 27 (2016), no. 3, 764-785. https://doi.org/10.1016/j.indag.2016.01.009
- A. M. Mathai and H. J. Haubold, Erdelyi-Kober fractional integral operators from a statistical perspective (I), Tbilisi Math. J. 10 (2017), no. 1, 145-159. https://doi.org/10.1515/tmj-2017-0009
- A. M. Mathai and H. J. Haubold, Erdelyi-Kober Fractional Calculus from a Statistical Perspective, Inspired by Solar Neutrino Physics, Springer Singapore, 2018.
- B. Opic and A. Kufner, Hardy-type inequalities, Pitman Research Notes in Mathematics Series, 219, Longman Scientific & Technical, Harlow, 1990.
- G. Pagnini, Erdelyi-Kober fractional diffusion, Fract. Calc. Appl. Anal. 15 (2012), no. 1, 117-127. https://doi.org/10.2478/s13540-012-0008-1
- L. Plociniczak, Approximation of the Erdelyi-Kober operator with application to the time-fractional porous medium equation, SIAM J. Appl. Math. 74 (2014), no. 4, 1219-1237. https://doi.org/10.1137/130942450
- L. Schwartz, Oeuvres de Jean Delsarte, Vols 1,2, Gothier-Villar, Paris, 1971.
- J. Shiue, A note on Cesaro function space, Tamkang J. Math. 1 (1970), no. 2, 91-95.
- I. N. Sneddon, The use in mathematical physics of Erdelyi-Kober operators and of some of their generalizations, in Fractional calculus and its applications (Proc. Internat. Conf., Univ. New Haven, West Haven, Conn., 1974), 37-79. Lecture Notes in Math., 457, Springer, Berlin, 1975.
- P. W. Sy, W. Y. Zhang, and P. Y. Lee, The dual of Ces'aro function spaces, Glas. Mat. Ser. III 22(42) (1987), no. 1, 103-112.
- T.-L. Yee and K.-P. Ho, Hardy's inequalities and integral operators on Herz-Morrey spaces, Open Math. 18 (2020), no. 1, 106-121. https://doi.org/10.1515/math-2020-0008