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

We obtain Hardy type inequalities $$int_0^infty {Mleft( {omega left( r right)left| {uleft( r right)} right|} right)rho left( r right)dr} leqslant C_1 int_0^infty {Mleft( {left| {uleft( r right)} right|} right)rho left( r right)dr + C_2 int_0^infty {Mleft( {left| {u'left( r right)} right|} right)rho left( r right)dr,} }$$ and their Orlicz-norm counterparts $$left| {omega u} right|_{L^M (mathbb{R}_ + ,rho )} leqslant tilde C_1 left| u right|_{L^M (mathbb{R}_ + ,rho )} + tilde C_2 left| {u'} right|_{L^M (mathbb{R}_ + ,rho )} ,$$ with an N-function M, power, power-logarithmic and power-exponential weights ??, ??, holding on suitable dilation invariant supersets of C ₀ ^?? (?₊). Maximal sets of admissible functions u are described. This paper is based on authors?? earlier abstract results and applies them to particular classes of weights.