New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights

作者：Kalmajska Agnieszka^*; Pietruska Paluba Katarzyna

来源：Central European Journal of Mathematics, 2012, 10(6): 2033-2050.

DOI：10.2478/s11533-012-0116-5

• Hardy inequalities
• Orlicz-Sobolev spaces
• Nondoubling measures

We obtain Hardy type inequalities %26lt;br%26gt;integral(infinity)(0) M(omega(r)vertical bar u(r)vertical bar)rho(r)dr %26lt;= C-1 integral(infinity)(0) M(vertical bar u(r)vertical bar)rho(r)dr + C-2 integral(infinity)(0) M(vertical bar u%26apos;(r)vertical bar)rho(r)dr, %26lt;br%26gt;and their Orlicz-norm counterparts %26lt;br%26gt;parallel to omega u parallel to(LM(R+,rho)) %26lt;= (C) over tilde (1)parallel to u parallel to(LM(R+,rho)) + (C) over tilde (2)parallel to u%26apos;parallel to(LM(R+,rho)), %26lt;br%26gt;with an N-function M, power, power-logarithmic and power-exponential weights omega,rho, holding on suitable dilation invariant supersets of C-0(infinity) (R+). Maximal sets of admissible functions u are described. This paper is based on authors%26apos; earlier abstract results and applies them to particular classes of weights.

• 出版日期2012-12