Discrete iterated Hardy-type inequalities with three weights

  • R. Oinarov L.N. Gumilyov Eurasian National University
  • B. Omarbayeva L.N. Gumilyov Eurasian National University
  • A. Temirkhanova L.N. Gumilyov Eurasian National University

Abstract

Discrete, continuous Hardy-typ e inequalities are of great imp ortance and have numerousapplications in harmonic analysis, in the theory of integral, differential and difference op erators,in the theory of emb eddings of function spaces and in other branches of mathematics. In recentyears, weighted estimates for multidimensional Hardy-typ e op erators have b een intensively studied,which have an imp ortant application in the study of b oundedness prop erties of op erators from aLeb esgue weighted space to a lo cal Morrey-typ e space, as well as in the study of bilinear op eratorsin Leb esgue weighted spaces. The discrete case of Hardy typ e inequalities with three weights is anop en problem. An inequality involving an iteration of the discrete Hardy op erator is traditionallyconsidered difficult to estimate b ecause it contains three indep endent weight sequences and threeparameters at their different ratios. In this pap er we prove some new discrete iterated Hardy-typ einequality involving three weights for the case 0 < p ≤ min { q , θ }.

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Published
2020-04-05
How to Cite
OINAROV, R.; OMARBAYEVA, B.; TEMIRKHANOVA, A.. Discrete iterated Hardy-type inequalities with three weights. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 105, n. 1, p. 19-29, apr. 2020. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/689>. Date accessed: 04 dec. 2020. doi: https://doi.org/10.26577/JMMCS.2020.v105.i1.03.
Keywords inequalities, Hardy-type operator, weight, sequences, discrete Lebesgue spaces