A sharp sparse domination of pseudodifferential operators

[1] T. Alazard, N. Burq and C. Zuily, A stationary phase type estimate, Proc. Amer. Math. Soc. 145 (2017),

2871–2880.

[2] K. Asada, On the L2 Boundedness of Fourier Integral Operators in Rn , Kodai Math. J. 7 (1984), no. 2,

248-272.

[3] D. Beltran. Control of pseudodifferential operators by maximal functions via weighted inequalities, Trans.

Amer. Math. Soc. 371 (2019), 3117-3143.

[4] D. Beltran and L. Cladek, Sparse bounds for pseudodifferential operators, J. Anal. Math. 140 (2020),

89–116.

[5] F. Bernicot, D. Frey and S. Petermichl, Sharp weighted norm estimates beyond Calder´

on-Zygmund theory,

Anal. PDE 9 (2016), no. 5, 1079-1113.

[6] H.-Q. Bui Weighted Besov and Triebel spaces: Interpolation by the real method, Hiroshima Math. J. 12

(1982), 581-605.

[7] R. M. Beals, Lp boundedness of Fourier integral operators, Mem. Amer. Math. Soc. 38 (1982), no. 264,

viii+57 pp.

[8] N. Bez, S. Lee, Sanghyuk and S. Nakamura, Strichartz estimates for orthonormal families of initial data

and weighted oscillatory integral estimates, Forum Math. Sigma 9 (2021), Paper No. e1, 52 pp.

[9] P. Brenner, On Lp -Lp estimates for the wave-equation, Math. Z. 145 (1975), no. 3, 251–254.

[10] S. M. Buckley, Estimates for operator norms on weighted spaces and reverse Jensen inequalities, Trans.

Amer. Math. Soc. 340 (1993), no. 1, 253–272.

[11] J. M. Conde-Alonso, A. Culiuc, F. Di. Plinio and Y. Ou, A sparse domination principle for rough singular

integrals, Anal. PDE 10 (2017), no. 5, 1255-1284.

[12] M. Cejas, K. Li, C. P´erez and I. P. Rivera-R´ıos, Vector-valued operators, optimal weighted estimates and

the Cp condition, Sci. China Math. 63 (2020), 1339–1368.

[13] S. Chanillo and A. Torchinsky, Sharp function and weighted Lp estimates for a class of pseudo-differential

operators, Ark. Math. 24 (1986) 1-25.

[14] A. P. Calder´on and R. Vaillancourt, A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci,

U.S.A., 69 (1972) 1185–1187.

[15] Y. Domar, On the spectral synthesis problem for (n − 1)-dimentional subsets of Rn , n ≥ 2, Ark. Mat. 9

(1971), 23–37.

[16] O. Dragiˇcevi´c, L. Grafakos, M. C. Pereyra, and S. Petermichl Extrapolation and sharp norm estimates for

classical operators on weighted Lebesgue spaces, Publ. Mat. 49 (2005), no. 1, 73–91.

[17] O. Elong and A. Senoussaoui, On the Lp -boundedness of a class of semiclassical Fourier integral operators,

Mat. Vesnik 70 (2018), no. 3, 189-203.

[18] C. Fefferman, Lp -bounds for pseudo-differential operators, Israel J. Math., 14 (1972) 413–417.

[19] L. H¨ormander, Pseudo-differential operators and hypoelliptic equations, In Proc. Symposium on Singular

Integrals, Amer. Math. Soc., Providence RI, 10 (1967) 138–183.

[20] L. H¨ormander Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79-183.

[21] T. P. Hyt¨onen, The sharp weighted bound for general Calde´

on-Zygmund operators, Ann. of Math. 175

(2012), no. 3, 1473-1506.

[22] T. P. Hyt¨onen, M. T. Lacey and C. P´erez Sharp weighted bounds for the q-variation of singular integrals.

Bull. Lond. Math. Soc. 45 (2013), no. 3, 529-540.

[23] T. P. Hyt¨onen and C. P´erez, Sharp weighted bounds involving A∞ , Anal. PDE, 6 (2013), no. 4, 777–818.

[24] M. T. Lacey and A. D. Mena, The sparse T1 theorem, Houston J. Math. 43 (2017), no. 1, 111-127.

[25] M. T. Lacey, K. Moen, C. P´ erez and R. H. Torres, Sharp weighted bounds for fractional integral operators,

J. Funct. Anal., 259(5):1073–1097, 2010.

[26] M. T. Lacey, A. D. Mena and M. C. Reguera Sparse Bounds for Bochner-Riesz Multipliers, J Fourier Anal

Appl 25 (2019), 523–537.

[27] A. K. Lerner, A simple proof of the A2 conjecture, Int. Math. Res. Not. 2013, no. 14, 3159-3170.

[28] A. K. Lerner, On pointwise estimates involving sparse operators, New York J. Math. 22 (2016), 341–349.

[29] A. K. Lerner A note on weighted bounds for rough singular integrals, C. R. Acad. Sci. Paris, Ser. I 356

(2018), 77–80.

[30] A. K. Lerner and F. Nazarov Intuitive dyadic calculus: The basics, Expo Math., 37 (2019), no. 3, 225-265.

[31] W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull.

Amer. Math. Soc. 69 (1963), 766–770.

[32] N. Miller, Weighted Sobolev spaces and pseudodifferential operators with smooth symbols, Trans. Amer.

Math. Soc. 269(1982), no. 1, 91–109.

[33] N. Michalowski, D. J. Rule and W. Staubach, Weighted norm inequalities for pseudo-pseudodifferential

operators defined by amplitudes, J. Funct. Anal. 258 (2010), no. 12, 4183–4209.

[34] N. Michalowski, D. J. Rule and W. Staubach Weighted Lp boundedness of pseudodifferential operators and

applications, Canad. Math. Bull., 55(2012), no. 3, 555–570.

[35] J. C. Peral, Lp estimates for the wave equation, J. Funct. Anal. 36 (1980), no. 1, 114-145.

[36] C. P´erez, S. Treil and A. Volberg, On A2 conjecture and corona decomposition of weights, arXiv:1006.2630.

[37] S. Petermichl, The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the

classical Ap - characteristic, Amer. J. Math., 129 (2007), no. 5, 1355–1375.

[38] S. Petermichl, The sharp weighted bound for the Riesz transforms, Proc. Amer. Math. Soc., 136 (2008),

no. 4, 1237–1249.

[39] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, With the

assistance of Timothy S. Murphy. Princeton Mathematical Series, 43. Monographs in Harmonic Analysis,

III.

[40] A. Seeger, C. D. Sogge and E. M. Stein, Regularity properties of Fourier integral operators, Ann. of Math.

(2) 134 (1991), no. 2, 231-251.

...