On Equivalent Conditions for the General Weighted Hardy Type Inequality in Space Lp(.)

Mamedov F. I., ZEREN Y.

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, vol.31, no.1, pp.55-74, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.4171/zaa/1448
  • Journal Name: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.55-74
  • Keywords: Hardy operator, Hardy inequality, variable exponents, weighted inequality, INTEGRAL CONDITIONS, THEOREM
  • Yıldız Technical University Affiliated: Yes

Abstract

We study the Hardy type two-weighted inequality for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L-p(.)(R-n) In tins way we prove equivalent conditions for L-P(.) -> L-q(.) boundedness of Hardy operator in the case of exponents q(0) >= p(0), q(infinity) >= p (infinity). We also prove that the condition for such inequality to hold coincides with condition for validity of two weighted Hardy inequalities with constant exponents, if we require the exponents to be regular near zero and at infinity.