Öz
Kaynakça
- [1] S. Chanillo, D. Watson and R.L. Wheeden, Some integral and maximal operators related to star-like, Studia Math. 107, 223–255, 1993.
- [2] Y. Ding and S. Lu, The $L^{p_1}\times\ldots\times L^{p_k}$ boundedness for some rough operators, J. Math. Anal. Appl. 203, 66–186, 1996.
- [3] Y. Ding and S. Lu, Weighted norm inequalities for fractional integral operators with rough kernel, Canad. J. Math. 50, 29–39 1998.
- [4] Y. Ding and S. Lu, Homogeneous fractional integrals on Hardy spaces, Tohoku Math. J. 52, 153–162, 2000.
- [5] A.D. Gadzhiev and I.A. Aliev, Riesz and Bessel potentials generated by the generalized shift operator and their inversions, (Russian) Theory of functions and approximations, Part 1 (Russian) (Saratov, 1988), 47–53, Saratov. Gos. Univ., Saratov, 1990.
- [6] V.S. Guliyev, A. Serbetci and I. Ekincioglu, On boundedness of the generalized Bpotential integral operators in the Lorentz spaces, Integral Transforms Spec. Funct. 18 (12), 885–895, 2007.
- [7] V.S. Guliyev, A. Serbetci and I. Ekincioglu, Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces, J. Math. Anal. Appl. 336 (1), 425–437, 2007.
- [8] V.S. Guliyev, A. Serbetci and I. Ekincioglu, The boundedness of the generalized anisotropic potentials with rough kernels in the Lorentz spaces, Integral Transforms Spec. Funct. 22 (12), 919–935, 2011.
- [9] I.A. Kipriyanov, Fourier-Bessel transformations and imbedding theorems, Trudy Math. Inst. Steklov, 89, 130–213, 1967.
- [10] B.M. Levitan, Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk. (Russian), 6 (2), 102–143, 1951.
- [11] L.N. Lyakhov, Multipliers of the Mixed Fourier-Bessel transform, Proc. Steklov Inst. Math. 214, 234–249, 1997.
- [12] B. Muckenhoupt and R.L. Wheeden, Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Math. Soc. 161, 249–258, 1971.
- [13] E.M. Stein, Singular Integrals And Differentiability Properties of Functions, Princeton New Jersey, Princeton Uni. Press, 1970.
- [14] E.M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, N. J., 1993.
- [15] E.M. Stein and G. Weiss, On the theory of harmonic functions of several variables I. The theory of Hp-spaces, Acta Math. 103, 25–62, 1960.
- [16] M.H. Taibleson and G.Weiss, The molecular characterization of certain Hardy spaces, Asterisque 77 Societe Math. de France, 67–149, 1980.
Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces
Öz
We prove the norm inequalities for potential operators and fractional integrals related to generalized shift operator defined on spaces of homogeneous type. We show that these operators are bounded from $H^{p}_{\Delta_{\nu}}$ to $H^{q}_{\Delta_{\nu}}$, for $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{Q}$, provided $0<\alpha<\frac{1}{2}$, and $\alpha<\beta\leq 1$ and $\frac{Q}{Q+\beta}<p\leq\frac{Q}{Q+\alpha}$. By applying atomic-molecular decomposition of $H^{p}_{\Delta_{\nu}}$ Hardy space, we obtain the boundedness of homogeneous fractional type integrals which extends the Stein-Weiss and Taibleson-Weiss's results for the boundedness of the $B_n$-Riesz potential operator on $H^{p}_{\Delta_{\nu}}$ Hardy space.
Anahtar Kelimeler
Laplace-Bessel operator generalized shift operator $B_n$-Riesz potential operator atomic-molecular decomposition Hardy space
Kaynakça
- [1] S. Chanillo, D. Watson and R.L. Wheeden, Some integral and maximal operators related to star-like, Studia Math. 107, 223–255, 1993.
- [2] Y. Ding and S. Lu, The $L^{p_1}\times\ldots\times L^{p_k}$ boundedness for some rough operators, J. Math. Anal. Appl. 203, 66–186, 1996.
- [3] Y. Ding and S. Lu, Weighted norm inequalities for fractional integral operators with rough kernel, Canad. J. Math. 50, 29–39 1998.
- [4] Y. Ding and S. Lu, Homogeneous fractional integrals on Hardy spaces, Tohoku Math. J. 52, 153–162, 2000.
- [5] A.D. Gadzhiev and I.A. Aliev, Riesz and Bessel potentials generated by the generalized shift operator and their inversions, (Russian) Theory of functions and approximations, Part 1 (Russian) (Saratov, 1988), 47–53, Saratov. Gos. Univ., Saratov, 1990.
- [6] V.S. Guliyev, A. Serbetci and I. Ekincioglu, On boundedness of the generalized Bpotential integral operators in the Lorentz spaces, Integral Transforms Spec. Funct. 18 (12), 885–895, 2007.
- [7] V.S. Guliyev, A. Serbetci and I. Ekincioglu, Necessary and sufficient conditions for the boundedness of rough B-fractional integral operators in the Lorentz spaces, J. Math. Anal. Appl. 336 (1), 425–437, 2007.
- [8] V.S. Guliyev, A. Serbetci and I. Ekincioglu, The boundedness of the generalized anisotropic potentials with rough kernels in the Lorentz spaces, Integral Transforms Spec. Funct. 22 (12), 919–935, 2011.
- [9] I.A. Kipriyanov, Fourier-Bessel transformations and imbedding theorems, Trudy Math. Inst. Steklov, 89, 130–213, 1967.
- [10] B.M. Levitan, Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk. (Russian), 6 (2), 102–143, 1951.
- [11] L.N. Lyakhov, Multipliers of the Mixed Fourier-Bessel transform, Proc. Steklov Inst. Math. 214, 234–249, 1997.
- [12] B. Muckenhoupt and R.L. Wheeden, Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Math. Soc. 161, 249–258, 1971.
- [13] E.M. Stein, Singular Integrals And Differentiability Properties of Functions, Princeton New Jersey, Princeton Uni. Press, 1970.
- [14] E.M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, N. J., 1993.
- [15] E.M. Stein and G. Weiss, On the theory of harmonic functions of several variables I. The theory of Hp-spaces, Acta Math. 103, 25–62, 1960.
- [16] M.H. Taibleson and G.Weiss, The molecular characterization of certain Hardy spaces, Asterisque 77 Societe Math. de France, 67–149, 1980.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Ekim 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 5 |