In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f...In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f = （fn）n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^＊=sup n≥0｜fn｜ adn f∞=lim n→∞ fn a.e.展开更多
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is ob...For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is obtained.展开更多
Let p>2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality■for a large class of non-symmetric Fourier multipliers T_(m) obtained via modulation of jumps of certain L...Let p>2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality■for a large class of non-symmetric Fourier multipliers T_(m) obtained via modulation of jumps of certain Lévy processes.In particular,the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane.The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle.Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.展开更多
We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhi...We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.展开更多
文摘In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f = （fn）n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^＊=sup n≥0｜fn｜ adn f∞=lim n→∞ fn a.e.
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
基金the National Natural Science Foundation of China (10771049 60773174)the Natural Science Foundation of Hebei Province (08M001)
文摘For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.12125109 and 11961131003)。
文摘Let p>2 be a given exponent.In this paper,we prove,with the best constant,the weak-type(p,p)inequality■for a large class of non-symmetric Fourier multipliers T_(m) obtained via modulation of jumps of certain Lévy processes.In particular,the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane.The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle.Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.
文摘We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.
