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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Our rst aim of this paper is to de ne maximal operators of a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ＜a < 1 by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.
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참고문헌 (19)
참고문헌 신청
D. Khoshnevisan / 2002 / Multiparameter Processes / Springer-Verlag
D. L. Burkholder / 1970 / Extrapolation and interpolation of Quasi-linear operators on martingales / Acta Math 124 (1) : 249 ~ 304
F. Schipp / 1992 / Universal contractive projections and a.e. convergence, Probability theory and applications / Math. Appl 80 : 221 ~ 233
F. Schipp / 1997 / Tree martingales and a.e. convergence of Vilenkin-Fourier series / Math. Pannon 8 (1) : 17 ~ 35
F. Weisz / 1994 / Martingale Hardy spaces and their applications in Fourier analysis, Lecture Notes in Mathematics / Springer-Verlag
D. L. Burkholder / 1970 / Extrapolation and interpolation of Quasi-linear operators on martingales / Acta Math 124 (1) : 249 ~ 304
F. Schipp / 1992 / Universal contractive projections and a.e. convergence, Probability theory and applications / Math. Appl 80 : 221 ~ 233
F. Schipp / 1997 / Tree martingales and a.e. convergence of Vilenkin-Fourier series / Math. Pannon 8 (1) : 17 ~ 35
F. Weisz / 1994 / Martingale Hardy spaces and their applications in Fourier analysis, Lecture Notes in Mathematics / Springer-Verlag
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