Geodesic
Boundedness of Littlewood-Paley operators relative to non-isotropic dilations
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 337-351
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We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $\Bbb R^n$. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^p$ spaces, $1
We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $\Bbb R^n$. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^p$ spaces, $1$, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).\looseness -1
DOI : 10.21136/CMJ.2018.0313-17
Classification : 42B25, 46E30
Keywords: Littlewood-Paley function; non-isotropic dilation 
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Sato, Shuichi. Boundedness of Littlewood-Paley operators relative to non-isotropic dilations. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 337-351. doi: 10.21136/CMJ.2018.0313-17

[1] Benedek, A., Calderón, A. P., Panzone, R.: Convolution operators on Banach space valued functions. Proc. Natl. Acad. Sci. USA 48 (1962), 356-365. | DOI | MR | JFM

[2] Calderón, A. P.: Inequalities for the maximal function relative to a metric. Stud. Math. 57 (1976), 297-306. | DOI | MR | JFM

[3] Calderón, A. P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. Adv. Math. 16 (1975), 1-64. | DOI | MR | JFM

[4] Capri, O. N.: On an inequality in the theory of parabolic $H^p$ spaces. Rev. Unión Mat. Argent. 32 (1985), 17-28. | MR | JFM

[5] Cheng, L. C.: On Littlewood-Paley functions. Proc. Am. Math. Soc. 135 (2007), 3241-3247. | DOI | MR | JFM

[6] Ding, Y., Sato, S.: Littlewood-Paley functions on homogeneous groups. Forum Math. 28 (2016), 43-55. | DOI | MR | JFM

[7] Duoandikoetxea, J.: Weighted norm inequalities for homogeneous singular integrals. Trans. Am. Math. Soc. 336 (1993), 869-880. | DOI | MR | JFM

[8] Duoandikoetxea, J.: Sharp $L^p$ boundedness for a class of square functions. Rev. Mat. Complut. 26 (2013), 535-548. | DOI | MR | JFM

[9] Duoandikoetxea, J., Francia, J. L. Rubio de: Maximal and singular integral operators via Fourier transform estimates. Invent. Math. 84 (1986), 541-561. | DOI | MR | JFM

[10] Duoandikoetxea, J., Seijo, E.: Weighted inequalities for rough square functions through extrapolation. Stud. Math. 149 (2002), 239-252. | DOI | MR | JFM

[11] Fan, D., Sato, S.: Remarks on Littlewood-Paley functions and singular integrals. J. Math. Soc. Japan 54 (2002), 565-585. | DOI | MR | JFM

[12] Garcia-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies 116, Notas de Matemática 104, North-Holland, Amsterdam (1985). | DOI | MR | JFM

[13] Hörmander, L.: Estimates for translation invariant operators in $L^p$ spaces. Acta Math. 104 (1960), 93-140. | DOI | MR | JFM

[14] Rivière, N.: Singular integrals and multiplier operators. Ark. Mat. 9 (1971), 243-278. | DOI | MR | JFM

[15] Francia, J. L. Rubio de: Factorization theory and $A_p$ weights. Am. J. Math. 106 (1984), 533-547. | DOI | MR | JFM

[16] Sato, S.: Remarks on square functions in the Littlewood-Paley theory. Bull. Aust. Math. Soc. 58 (1998), 199-211. | DOI | MR | JFM

[17] Sato, S.: Estimates for Littlewood-Paley functions and extrapolation. Integral Equations Oper. Theory 62 (2008), 429-440. | DOI | MR | JFM

[18] Sato, S.: Estimates for singular integrals along surfaces of revolution. J. Aust. Math. Soc. 86 (2009), 413-430. | DOI | MR | JFM

[19] Sato, S.: Littlewood-Paley equivalence and homogeneous Fourier multipliers. Integral Equations Oper. Theory 87 (2017), 15-44. | DOI | MR | JFM

[20] Stein, E. M.: Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series 30, Princeton University Press, Princeton (1970). | DOI | MR | JFM

[21] Stein, E. M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Am. Math. Soc. 84 (1978), 1239-1295. | DOI | MR | JFM

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