Abstract
Abstract Let p∈[1,∞), 0≤ q∈ L 1 loc (R). Consider an equation-y′(x)+ q (x) y (x)= f (x), x∈ R where f∈ L p (ℝ), and the weight function space S p (1)(R, q)={y∈ AC loc (R):∥ y′-qy∥ L p [(R)+∥ q 1/py∥ L p (R)<∞}. The following assertion is the main result of the paper:
Theorem. Equation (0.1) is correctly solvable in L p (ℝ), p∈[1,∞) if and only if the space S p(1)(ℝ, q) is embedded into L p (ℝ).
Theorem. Equation (0.1) is correctly solvable in L p (ℝ), p∈[1,∞) if and only if the space S p(1)(ℝ, q) is embedded into L p (ℝ).
| Original language | American English |
|---|---|
| Pages (from-to) | 1-17 |
| Journal | Analysis |
| Volume | 34 |
| Issue number | 1 |
| State | Published - 2014 |