Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operator

Ayazoglu R., Ekincioglu I., Şener S. Ş.

FILOMAT, cilt.36, sa.10, ss.3321-3330, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 10
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2210321a
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.3321-3330
  • Anahtar Kelimeler: Approximation, Hardy averaging operator, Power-type weighted Sobolev spaces with variable exponent, Power-type weighted grand Lebesgue spaces with variable exponent, KANTOROVICH OPERATORS, UNIFORM BOUNDEDNESS, MAXIMAL-FUNCTION, LEBESGUE SPACES, INEQUALITIES
  • Atatürk Üniversitesi Adresli: Evet

Özet

We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), (r = 1, 2,...), by the Hardy averaging operator A (f) (x) = 1/x integral(x)(0) f (t)dt. If the function f lies in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), it is shown that