A necessary and sufficient condition for Hardy's operator in Lp(.)(0,1)

作者：Mamedov Farman I^*; Mammadova Firana M

来源：Mathematische Nachrichten, 2014, 287(5-6): 666-676.

DOI：10.1002/mana.201200291

• The Hardy operator
• variable exponent
• weighted inequality
• necessary and sufficient condition
• 42A05
• 42B25
• 26D10
• 35A2

The equivalent conditions are proved for the Hardy inequality
parallel to x(beta(.)-1) integral(x)(0) f(t) dt parallel to(Lp(.)(0, 1)) <= C parallel to(x beta(.)) f parallel to(Lp(.)(0, 1)), f >= 0,
to be fulfilled in the norms of a Lebesgue space with variable exponent L-p(.)(0, 1). It is assumed that the function 1/beta(.)-p '(.) is monotone and positive on (0, 1).

• 出版日期2014-4