Some applications of the a-Duhamel product

GÜRDAL M., Garayev M., Tapdigoglu R., Altintas M.

JOURNAL OF ANALYSIS, no.2, pp.1557-1572, 2023 (ESCI) identifier

  • Nəşrin Növü: Article / Article
  • Nəşr tarixi: 2023
  • Doi nömrəsi: 10.1007/s41478-022-00539-2
  • jurnalın adı: JOURNAL OF ANALYSIS
  • Jurnalın baxıldığı indekslər: Emerging Sources Citation Index (ESCI)
  • Səhifə sayı: pp.1557-1572
  • Adres: Bəli

Qısa məlumat

We consider the space C-(n) (omega), the Banach space of continuous functions with n derivatives and the n th derivative continuous in omega, where omega subset of C is a starlike region with respect to a alpha is an element of omega. We use the so-called alpha-Duhamel product (f circle times g(alpha))(z) := d/dz integral(z)(alpha) f(z+alpha-t)g(t)dt = d/dz (f*g(alpha)) (z) to describe usual *-generators of the Banach algebra C-(n) (omega),(alpha)* to estimate ||(I -V-a)(m)|| and to estimate below the norm dm , where V-a is the Volterra inte-A z gration operator defined by V(a)f (z) = integral(z)(alpha)f (t)dt and delta A is the inner derivation operator a defined by delta(A) (X) := [X, A]. We give a new proof of Aleman-Korenblum theorem in one particular case. Namely, we describe V-invariant subspaces in the Hardy space H(p )by using Duhamel product.