Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space

Abstract

For the integral operator , x ∈ (a, b) ⊆ ℝ, under some assumptions on the kernel K(x, t) ≥ 0 we find necessary and sufficient conditions for the validity of the following weighted inequality

where A^○C(a, b) is a set of absolutely continuous functions with compact supports

Keywords:

• boundedness of integral operators
• Hardy operator with variable integration limits
• Sobolev space
• weighted embedding
• dual inequality

AMS Subject Classifications::

• Primary 26D10
• Secondary 26D15
• 26D07