On the Boundedness of the Generalized Translation Operator on Variable Exponent Lebesgue Spaces

Ekincioglu I., Shishkina E. L., KAYA E.

Acta Applicandae Mathematicae, cilt.173, sa.1, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 173 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s10440-021-00411-8
  • Dergi Adı: Acta Applicandae Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Compendex, MathSciNet, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Generalized translation operator, Laplace-Bessel operator, Variable exponent Lebesgue spaces
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Hayır

Özet

In this paper we are deal with the generalized translation operator generated by the Bessel operator in variable exponent Lebesgue spaces. The behavior of this generalized translation operator is well known on weighted Lebesgue spaces. But, there are some differences in the behavior of these operators on the variable exponent Lebesgue spaces. For example, the generalized translation operator is bounded in the variable exponent Lebesgue space Lp(⋅),γ(R+n) if and only if the exponent is constant. The aim of this paper is to give some the regularity conditions which ensure the boundedness of generalized translation operator Ty on variable exponent Lebesgue spaces if p is nonconstant.