Adam Osękowski

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Publications

2012

• A. Osękowski, On the best constants in the weak type inequalities for re-expansion operator and Hilbert transform, Transactions of the American Mathematical Society 364 (2012), pp. 4303--4322. (original pdf)
• A. Osękowski, Sharp logarithmic inequalities for Riesz transforms, Journal of Functional Analysis 263 (2012), pp. 89--108. (original pdf)
• A. Osękowski, Weak type (p,q)-inequalities for the Haar system and differentially subordinated martingales, Mathematische Nachrichten 285 (2012), pp. 794--807. (original pdf)
• A. Osękowski, Doob-type estimates for differentially subordinated martingales, Stochastic Analysis and Applications 30 (2012), pp. 426--447. (original pdf)
• A. Osękowski, A note on Burkholder-Rosenthal inequality, Bulletin of the Polish Academy of Sciences Mathematics 60 (2012), pp. 177--185. (original pdf)
• A. Osękowski, Sharp weak type inequalities for the Haar system and related estimates for non-symmetric martingale transforms, Proceedings of the American Mathematical Society 140 (2012), pp. 2513--2526. (original pdf)
• A. Osękowski, Best constants in the weak type inequalities for a martingale conditional square function, Statistics and Probability Letters 82 (2012), pp. 885--893. (original pdf)
• A. Osękowski, Best constant in Zygmund's inequality and related estimates for orthogonal harmonic functions and martingales, Journal of the Korean Mathematical Society 49 (2012), pp. 659--670. (original pdf)
• A. Osękowski, Logarithmic estimates for the Hilbert transform and the Riesz projection, Archiv der Mathematik 98 (2012), pp. 153--161. (original pdf)
• R. Bañuelos, A. Osękowski, Martingales and sharp bounds for Fourier multipliers, Annales Academiae Scientiarum Fennicae Mathematica 37 (2012), pp. 251--263. (original pdf)
• A. Osękowski, Weak norm inequalities for martingales and geometry of Banach spaces, Statistics and Probability Letters 82 (2012), pp. 411--418. (original pdf).
• A. Osękowski, Inequalities for martingale transforms and related characterizations of Hilbert spaces, Statistics and Probability Letters 82 (2012), pp. 186--190. (original pdf)

2011

• A. Osękowski, A weak-type inequality for orthogonal submartingales and subharmonic functions, Bulletin of the Polish Academy of Sciences Mathematics 59 (2011), pp. 261--274. (original pdf)
• A. Osękowski, A sharp weak-type bound for Ito processes and subharmonic functions, Kyoto Journal of Mathematics 51 (2011), pp. 875--890. (original pdf)
• A. Osękowski, Weak type inequality for the martingale square function and a related characterization of Hilbert spaces, Probability and Mathematical Statistics 31 (2011), pp. 227--238. (original pdf)
• A. Osękowski, Sharp maximal inequalities for the moments of martingales and nonnegative submartingales, Bernoulli Journal of Mathematics 17 (2011), pp. 1327--1343. (original pdf).
• A. Osękowski, On relaxing the assumption of differential subordination in some martingale inequalities, Electronic Communications in Probability 16 (2011), pp. 9--21. (original pdf)
• A. Osękowski, Maximal inequalities for continuous martingales and their differential subordinates, Proceedings of the American Mathematical Society 139 (2011), pp. 721--734. (original pdf)
• A. Osękowski, Sharp and strict L^p-inequalities for Hilbert-space-valued orthogonal martingales, Electronic Journal of Probability 16 (2011), pp. 531--551. (original pdf)
• A. Osękowski, A maximal inequality for nonnegative sub- and supermartingales, Mathematical Inequalities and Applications 14 (2011), pp. 595--604. (original pdf).
• A. Osękowski, Logarithmic estimates for submartingales and their differential subordinates , Journal of Theoretical Probability 24 (2011), pp. 849--874. (original pdf).
• A. Osękowski, Sharp maximal inequality for nonnegative martingales, Statistics and Probability Letters 81 (2011), pp. 1945--1952. (original pdf).

2010

• A. Osękowski, Sharp inequality for martingale maximal functions and stochastic integrals, Illinois Journal of Mathematics, volume in honour of Donald L. Burkholder 54 (2010), pp. 1133--1156. (original pdf).
• A. Osękowski, Maximal inequalities for stochastic integrals, Bulletin of the Polish Academy of Sciences Mathematics 58 (2010), pp. 273--287. (original pdf).
• A. Osękowski, Sharp maximal inequalities for the martingale square bracket, Stochastics: An International Journal of Probability and Stochastic Processes 82 (2010), pp. 589--605. (original pdf)
• A. Osękowski, Sharp moment inequalities for differentially subordinated martingales, Studia Mathematica 201 (2010), pp. 103--131. (original pdf)
• A. Osękowski, Weak type inequalities for conditionally symmetric martingales, Statistics and Probability Letters 80, Vol. 8 (2010), pp. 2009--2013. (original pdf)
• A. Osękowski, Sharp tail inequalities for nonnegative submartingales and their strong differential subordinates, Electronic Communications in Probability 15 (2010), pp. 508--521. (original pdf)
• A. Osękowski, Sharp inequalities for sums of nonnegative random variables and for a martingale conditional square function, ALEA: Latin American Journal of Probability and Mathematical Statistics 7 (2010), pp. 243--256. (original pdf)
• A. Osękowski, Sharp maximal bound for continuous martingales, Statistics and Probability Letters 80, Vol. 4 (2010), pp. 1405--1408. (original pdf)
• A. Osękowski, Sharp ratio inequalities for a conditionally symmetric martingale, Bulletin of the Polish Academy of Sciences Mathematics 58, Vol. 1 (2010), pp. 65--77. (original pdf).
• A. Osękowski, Sharp inequalities for the square function of a nonnegative martingale, Probability and Mathematical Statistics 30, Vol. 1 (2010), pp. 61--72. (original pdf).
• A. Osękowski, Logarithmic estimates for nonsymmetric martingale transforms, Statistics and Probability Letters 80, Vol. 4 (2010), pp. 678--682. (original pdf)

2009

• A. Osękowski, Strong differential subordination and sharp inequalities for orthogonal processes , Journal of Theoretical Probability 22, Vol. 4 (2009), pp. 837--855. (original pdf)
• A. Osękowski, Sharp weak type inequalities for differentially subordinated martingales, Bernoulli Journal of Mathematics 15, Vol. 3 (2009), pp. 871--897. (original pdf)
• A. Osękowski, Sharp norm comparison of the maxima of a sequence and its predictable projection, Statistics and Probability Letters 79 Vol. 16 (2009), pp. 1784--1788. (original pdf)
• A. Osękowski, Weak type inequality for the square function of a nonnegative submartingale , Bulletin of the Polish Academy of Sciences Mathematics 57, Vol. 1 (2009), pp. 81--89. (original pdf)
• A. Osękowski, On the best constant in the weak type inequality for the square function of a conditionally symmetric martingale, Statistics and Probability Letters 79 (2009), pp. 1536--1538. (original pdf)
• A. Osękowski, Sharp norm inequalities for Stochastic integrals in which the integrator is a nonnegative supermartingale, Probability and Mathematical Statistics 29, Vol. 1 (2009), pp. 29--42. (original pdf)
• A. Osękowski, Sharp Maximal Inequality for Martingales and Stochastic Integrals, Electronic Communications in Probability 14 (2009), pp. 17--30. (original pdf)

2008

• A. Osękowski, Sharp LlogL inequality for Differentially Subordinated Martingales, Illinois Journal of Mathematics 52, Vol. 3 (2008), pp. 745--756. (original pdf)
• A. Osękowski, Sharp inequality for bounded submartingales and their differential subordinates, Electronic Communications in Probability 13 (2008), pp. 660--675. (original pdf)
• A. Osękowski, Sharp norm inequality for bounded submartingales, Journal of Inequalities in Pure and Applied Mathematics (JIPAM) 9 Vol. 4 (2008), art. 93. (original pdf)
• A. Osękowski, On Φ-inequalities for Bounded Submartingales and Subharmonic Functions, Communications of the Korean Mathematical Society 23, Vol. 2 (2008) , pp. 269--277. (original pdf)
• A. Osękowski, Weak type inequality for noncommutative differentially subordinated martingales, Probability Theory and Related Fields 140 (2008), pp. 553 -- 568. (original pdf)
• A. Osękowski, Sharp maximal inequality for stochastic integrals, Proceedings of the American Mathematical Society 136 (2008), pp. 2951--2958. (original pdf)

2007

• A. Osękowski, Sharp Norm Inequalities for Martingales and their Differential Subordinates, Bulletin of the Polish Academy of Sciences Mathematics 55 (2007), pp. 373--385. (original pdf)
• A. Osękowski, Inequalities for dominated martingales, Bernoulli Journal of Mathematics 13, Vol. 1 (2007), pp. 54--79. (original pdf)

2005

• A. Osękowski, Two inequalities for the first moment of a martingale, its square and maximal function, Bulletin of the Polish Academy of Sciences Mathematics 53 (2005), pp. 441--449. (original pdf)

Publications to appear

• R. Bañuelos, A. Osękowski, Sharp inequalities for the Beurling-Ahlfors transform on radial functions, to appear in Duke Mathematical Journal.
• A. Osękowski, Sharp inequalities for the dyadic square function in the BMO setting, to appear in Acta Mathematica Hungarica.
• A. Osękowski, Sharp estimates for the functions of bounded lower oscillation, to appear in Bulletin of the Australian Mathematical Society.
• A. Osękowski, Sharp maximal inequalities for continuous-path semimartingales, to appear in Mathematical Inequalities and Applications.
• A. Osękowski, Best constants in the weak-type estimates for uncentered maximal operators, to appear in Glasgow Mathematical Journal.
• A. Osękowski, Logarithmic inequalities for Fourier multipliers, to appear in Mathematische Zeitschrift.
• A. Osękowski, Sharp martingale and semimartingale inequalities, to appear in Monografie Matematyczne, Birkhäuser.
• R. Bañuelos, A. Osękowski, Burkholder inequalities for submartingales, Bessel processes and conformal martingales, to appear in American Journal of Mathematics.
• A. Osękowski, Sharp weak type inequalities for Hilbert transform and Riesz projection, to appear in Israel Journal of Mathematics.
• A. Osękowski, Sharp inequalities for differentially subordinate harmonic functions and martingales, to appear in Canadian Mathematical Bulletin.