Boundedness of Riesz potential generated by generalized shift operator on B a spaces

Ayhan Ṣerbetci; Ismail Ekincioğlu

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 3, page 579-589
  • ISSN: 0011-4642

Abstract

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In this paper, the boundedness of the Riesz potential generated by generalized shift operator I B k α from the spaces a = ( L p m , ν ( n k ) , a m ) to the spaces a ' = ( L q m , ν ( n k ) , a m ' ) is examined.

How to cite

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Ṣerbetci, Ayhan, and Ekincioğlu, Ismail. "Boundedness of Riesz potential generated by generalized shift operator on $Ba$ spaces." Czechoslovak Mathematical Journal 54.3 (2004): 579-589. <http://eudml.org/doc/30884>.

@article{Ṣerbetci2004,
abstract = {In this paper, the boundedness of the Riesz potential generated by generalized shift operator $I^\{\alpha \}_\{B_\{k\}\}$ from the spaces $\{a = (L_\{p_\{m\}, \nu \} (\mathbb \{R\}_n^k), a_m)\}$ to the spaces $\{a^\{\prime \}= (L_\{q_\{m\}, \nu \} (\mathbb \{R\}_n^k), a^\{\prime \}_m)\}$ is examined.},
author = {Ṣerbetci, Ayhan, Ekincioğlu, Ismail},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized shift operator; Riesz-Bessel transformations; generalized shift operator; Riesz-Bessel transformations},
language = {eng},
number = {3},
pages = {579-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of Riesz potential generated by generalized shift operator on $Ba$ spaces},
url = {http://eudml.org/doc/30884},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Ṣerbetci, Ayhan
AU - Ekincioğlu, Ismail
TI - Boundedness of Riesz potential generated by generalized shift operator on $Ba$ spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 3
SP - 579
EP - 589
AB - In this paper, the boundedness of the Riesz potential generated by generalized shift operator $I^{\alpha }_{B_{k}}$ from the spaces ${a = (L_{p_{m}, \nu } (\mathbb {R}_n^k), a_m)}$ to the spaces ${a^{\prime }= (L_{q_{m}, \nu } (\mathbb {R}_n^k), a^{\prime }_m)}$ is examined.
LA - eng
KW - generalized shift operator; Riesz-Bessel transformations; generalized shift operator; Riesz-Bessel transformations
UR - http://eudml.org/doc/30884
ER -

References

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  7. On Boundedness of Riesz Transform and the Riesz Potential in B a Spaces, Theory of B a spaces and its applications, Science Press, Beijing, 1999, pp. 63–72. (1999) MR1414957
  8. On a potential like operators generated by the generalized shift operator, Vekua Inst. Applied Math. 3 (1988), 21–24. (1988) 
  9. On high order Riesz transformations generated by a generalized shift operator, Tr. J. Math. 21 (1997), 51–60. (1997) MR1473300
  10. On the singular integral operators generated by the generalized shift operator, Int. J. App. Math. 1 (1999), 29–38. (1999) MR1689693
  11. Bessel function expansions in series and fourier integrals, Uspekhi Mat. Nauk 6 (1951), 102–143. (1951) MR0049376
  12. Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970. (1970) Zbl0207.13501MR0290095

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