Weights of exponential growth and decay for Schrödinger-type operators

Fix d≥3 and 10⁡e−tLV|f| are bounded on weighted Lebesgue space Lp(w). The boundedness LV-Riesz potentials LV−α/2 from Lp(w) Lν(wν/p) 0<α≤2, 1<p<dα 1ν=1p−αd will also be proved. These weight strictly larger than a previously introduced by Bongioanni, Harboure Salinas in [8] that shares these properties they contain exponential growth decay. considered relation different generalised forms operator. particular, with measure potential −Δ+μ, uniformly elliptic −divA∇+V magnetic (∇−ia)⁎(∇−ia)+V all considered. Finally, article investigate necessary conditions must satisfy order or To aid task, lower bounds kernel standard −Δ+V estimates provide counterpart upper proved [23].