Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 757-773

FRACTIONAL DERIVATIVES OF POINTWISE MULTIPLIERS BETWEEN HOLOMORPHIC SPACES

Carme Cascante, Joan Fàbrega and Joaquin M. Ortega

Universitat de Barcelona, Departament Matemàtica Aplicada i Anàlisi
Gran Via 585, 08071 Barcelona, Spain; cascante 'at' ub.edu

Universitat de Barcelona, Departament Matemàtica Aplicada i Anàlisi
Gran Via 585, 08071 Barcelona, Spain; joan_fabrega 'at' ub.edu

Universitat de Barcelona, Departament Matemàtica Aplicada i Anàlisi
Gran Via 585, 08071 Barcelona, Spain; ortega 'at' ub.edu

Abstract. We study the action of fractional differential type operators on the space of pointwise multipliers between holomorphic Triebel-Lizorkin spaces on the unit ball B of Cⁿ. As an application, we obtain new characterizations and examples of multipliers on Hardy-Sobolev spaces, and we improve some well-known results about the integrals operators I_b and J_b.

2010 Mathematics Subject Classification: Primary 47B35, 32A37, 47G10.

Key words: Triebel-Lizorkin spaces, pointwise multipliers, integral operators.

Reference to this article: C. Cascante, J. Fàbrega and J.M. Ortega: Fractional derivatives of pointwise multipliers between holomorphic spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 757-773.

Full document as PDF file

doi:10.5186/aasfm.2016.4149