Weighted Hardy-type inequality in two dimensions
-
Rohit Chauhan
Abstract
Weighted Hardy-type inequality in two dimensions has been characterized for pairs of weight functions
Acknowledgements
We are gratefully acknowledges to the editor and anonymous referees for their valuable remarks, which helped to improve the paper.
References
[1] J. Appell and A. Kufner, On the two-dimensional Hardy operator in Lebesgue spaces with mixed norms, Analysis 15 (1995), no. 1, 91–98. 10.1524/anly.1995.15.1.91Search in Google Scholar
[2] B. Benaissa and M. Z. Sarikaya, Some Hardy-type integral inequalities involving functions of two independent variables, Positivity 25 (2021), no. 3, 853–866. 10.1007/s11117-020-00791-5Search in Google Scholar
[3] H. P. Heinig, R. Kerman and M. Krbec, Weighted exponential inequalities, Georgian Math. J. 8 (2001), no. 1, 69–86. 10.1515/GMJ.2001.69Search in Google Scholar
[4] V. Kokilashvili, L.-E. Persson and A. Meskhi, Weighted Norm Inequalities for Integral Transforms with Product Kernels, Nova Science Publishers, New York, 2009. Search in Google Scholar
[5] A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientific, Singapore, 2003. 10.1142/5129Search in Google Scholar
[6] S. Kumar, A Hardy-type inequality in two dimensions, Indag. Math. (N. S.) 20 (2009), no. 2, 247–260. 10.1016/S0019-3577(09)80012-8Search in Google Scholar
[7] A. Meskhi, On two-weight inequalities for multiple Hardy-type operators, Proc. A. Razmadze Math. Inst. 136 (2004), 149–153. Search in Google Scholar
[8] A. Meskhi, A note on two-weight inequalities for multiple Hardy-type operators, J. Funct. Spaces Appl. 3 (2005), no. 3, 223–237. 10.1155/2005/361878Search in Google Scholar
[9] B. Muckenhoupt, Weighted norm inequalities for classical operators, Harmonic Analysis in Euclidean Spaces, Proc. Sympos. Pure Math. 35, American Mathematical Society, Providence (1979), 69–83. 10.1090/pspum/035.1/545240Search in Google Scholar
[10] B. Muckenhoupt, Hardy’s inequality with weights in two dimensions, Notices Amer. Math. Soc. 29 (1982), no. 6, Paper No. 538. Search in Google Scholar
[11] B. Muckenhoupt, Weighted norm inequalities for the Fourier transform, Trans. Amer. Math. Soc. 276 (1983), no. 2, 729–742. 10.1090/S0002-9947-1983-0688974-XSearch in Google Scholar
[12] E. Sawyer, Weighted inequalities for the two-dimensional Hardy operator, Studia Math. 82 (1985), no. 1, 1–16. 10.4064/sm-82-1-1-16Search in Google Scholar
[13] V. D. Stepanov and E. P. Ushakova, On weighted Hardy inequality with two-dimensional rectangular operator—extension of the E. Sawyer theorem, Math. Inequal. Appl. 24 (2021), no. 3, 617–634. 10.7153/mia-2021-24-43Search in Google Scholar
[14] V. D. Stepanov and E. P. Ushakova, Boundedness and compactness of the two-dimensional rectangular Hardy operator, Dokl. Math. 106 (2022), no. 2, 361–365. 10.1134/S1064562422050180Search in Google Scholar
[15] A. Wedestig, Weighted inequalities for the Sawyer two-dimensional Hardy operator and its limiting geometric mean operator, J. Inequal. Appl. 2005 (2005), no. 4, 387–394. 10.1155/JIA.2005.387Search in Google Scholar
[16] P. A. Zharov, On a two-weight inequality. Generalization of Hardy and Poincaré inequalities, Trudy Mat. Inst. Steklov. 194 (1992), 97–110. Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
