In this paper, we study the high-dimensional Hausdorff operators, defined via a general linear mapping A, and their commutators on the weighted Morrey spaces in the setting of the Heisenberg group. Particularly, under some assumption on the mapping A, we establish their sharp boundedness on the power weighted Morrey spaces.
Abstract. In this paper, we study the high-dimensional Hausdorff operators on the weighted Herz-type Hardy spaces and obtain some substantial extensions from the previous results in [3]. Particularly, for the Hausdorff operators, we establish their sharp boundedness on the power weighted Herz-type Hardy spaces. Our results reveal that the Housdorff operators have better performance in the Herz-type Hardy spaces HKq (R n ;w) ) than their performance in the Hardy spaces H p (R n ;w) ( h p (R n ;w) ) when 0 < p < 1 .Mathematics subject classification (2010): 42B30, 42B35.
In this paper, we give some characterizations of h -convex functions, and some applications related to these functions are also obtained. According to these results, we can know better the relation between convex functions and h -convex functions.
In this paper, the Hermite-Hadamard type inequalitis for Riemann-Liouville fractional integrals via strongly h -convex functions are established. Furthermore, we obtain some identities related to the fractional integrals with n -times differentiable functions, and then gain midpoint type and trapezoid type error estimates connected with the Hermite-Hadamard type inequalities, which generalize some known results.
In this paper, we are interested in the following bilinear fractional integral operator BI α defined by BI α (f ,g)(x) = R n f (x − y)g(x + y) |y| n−α dy, with 0 < α < n. We prove the weighted boundedness of BI α on the Morrey type spaces. Moreover, an Olsen type inequality for BI α is also given.
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