THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS

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Gadjiev A. D., Guliyev V. S., ŞERBETÇİ A., Guliyev E. V.

JOURNAL OF MATHEMATICAL INEQUALITIES, cilt.5, sa.1, ss.87-106, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2011
  • Doi Numarası: 10.7153/jmi-05-09
  • Dergi Adı: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.87-106
  • Anahtar Kelimeler: Laplace-Bessel differential operator, B-Riesz potential, Stein-Weiss type inequalities, weighted Lebesgue space, weighted B-Besov space, FRACTIONAL INTEGRALS, BOUNDEDNESS, OPERATORS
  • Ankara Üniversitesi Adresli: Evet

Özet

We establish two inequalities of Stein-Weiss type for the Riesz potential operator I-alpha,I-gamma (B-Riesz potential operator) generated by the Laplace-Bessel differential operator Delta B in the weighted Lebesgue spaces L-p,L-vertical bar x vertical bar beta,L-gamma. We obtain necessary and sufficient conditions on the parameters for the boundedness of Ia,. from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to L-q,L-vertical bar x vertical bar-lambda,L-gamma, and from the spaces L-1,L-vertical bar x vertical bar beta,L-gamma to the weak spaces WLq,vertical bar x vertical bar-lambda,gamma. In the limiting case p = Q/alpha we prove that the modified B-Riesz potential operator (I) over tilde (alpha,gamma) is bounded from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to the weighted B-BMO spaces BMO vertical bar x vertical bar-lambda,gamma.