Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 899–902

MULTILINEAR FRACTIONAL INTEGRAL OPERATORS: A COUNTER-EXAMPLE

Pablo Rocha

Universidad Nacional del Sur, Departamento de Matemática
Av. Alem 1253 - Bahía Blanca 8000, Buenos Aires, Argentina; pablo.rocha 'at' uns.edu.ar

Abstract. By means of a counter-example we show that the multilinear fractional operator I_γ (1 < γ < 2) is not bounded from H¹(R) × H^p(R) into H^q(R), for 0 < p ≤ γ^-1 and 1/q = 1 + 1/p – γ.

2010 Mathematics Subject Classification: Primary 42B20, 42B30.

Key words: Multilinear fractional operators, Hardy spaces.

Reference to this article: P. Rocha: Multilinear fractional integral operators: a counter-example. Ann. Acad. Sci. Fenn. Math. 45 (2020), 899–902.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4549