| Abstract: |
| We will discuss how to define and characterize one-sided weighted Sobolev spaces which capture the one-sided nature of fractional derivatives. Even for left and right `classical` derivatives, defined by the one-sided limits of the difference quotient, the one-sided property is lost in the weak sense. We will build up a one-sided distributional setting and consider weighted Sobolev spaces with one-sided Sawyer weights. The pointwise and norm limits as the orders of the derivatives converge to an integer are also analyzed. This is joint work with my advisor Pablo Ra\`ul Stinga (Iowa State University). |
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