Orlicz–Morrey Spaces and Fractional Operators

By taking an interest in a natural extension to the small parameters of the trace inequality for Morrey spaces, Orlicz–Morrey spaces are introduced and some inequalities for generalized fractional integral operators on Orlicz–Morrey spaces are established. The local boundedness property of the Orlicz maximal operators is investigated and some Morrey-norm equivalences are also verified. The result obtained here sharpens the one in our earlier papers.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Potential Operators,Maximal Functions,and Generalizations of A ∞

We derive weighted norm estimates which relate integral operators of potential type (fractional integrals) to corresponding maximal operators (fractional maximal operators). We also derive norm estimates for the maximal operators. The conditions that we impose on the weights involve A conditions of content type which are weaker than the usual A condition. The analysis is carried out in the context of spaces of homogeneous type.     

On Weighted α-Besov Spaces and α-Bloch Spaces of Quaternion-Valued Functions

In this paper, we give the definitions of weighted α-Besov-type spaces and α-Bloch spaces of quaternion-valued functions, then we obtain characterizations of these quaternion α-Bloch spaces by quaternion α-Besov-type spaces. Relations between Q _p norms and weighted α-Besov norms are also considered. The role of ρ?^α sequences in securing non-Bloch functions is highlighted in quaternion sense.     

Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators

Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.     

Fuzzy φψ-continuous Functions between L-topological Spaces (Ⅱ)

In the present paper, sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a family of L-topological spaces into L-topological spaces are investigated.     

Landau–Bloch Constants for Functions in α-Bloch Spaces and Hardy Spaces

In this paper, we obtain a sharp distortion theorem for a class of functions in ??-Bloch spaces, and as an application of it, we establish the corresponding Landau??s theorem. These results generalize the corresponding results of Bonk, Minda and Yanagihara, and Liu, respectively. We also prove the existence of Landau?CBloch constant for a class of functions in Hardy spaces and the obtained result is a generalization of the corresponding result of Chen and Gauthier.     

Vector Spaces of Non-measurable Functions

We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.     

Fractional Operators on Morrey—Lorentz Spaces and the Olsen Inequality

Mathematical Notes - Under the Morrey norm, the fractional integral operator and the fractional maximal operator behave similarly as was initially proved by Adams and Xiao. Later on, Tanaka...     

Fractional square functions and potential spaces

Carlos Segovia and Richard Wheeden defined fractional square functions involving fractional derivatives. They obtained characterizations of potential spaces via square functions. Our aim in this paper is to reconsider the ideas of Segovia and Wheeden under the light of the semigroups of operators. We develop a quite general theory of fractional square functions associated to certain classes of operators. We present some examples of differential operators where our theory applies. We recover in a more compact way the results of Segovia and Wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and Ornstein–Uhlenbeck operators.     

Boundedness of Area Functions Related to Schrödinger Operators and Their Commutators in Weighted Hardy Spaces

In this paper, we consider the area function $S_Q$ related to the Schrödinger operator $\mathcal{L}$ and its commutator $S_{Q,b}$, establish the boundedness of $S_Q$ from $H^p_\rho(w)$ to $L^p(w)$ or $WL^p(w),$ as well as the boundedness of $S_{Q,b}$ from $H^1_\rho(w)$ to $WL^1(w).$     

Boundedness of Commutators Generated by Campanato-type Functions and Riesz Transforms Associated with Schrdinger Operators

Let■=-△+V be a Schrdinger operator on R~n,n3,where △is the Laplacian on R~n and V≠0 is a nonnegative function satisfying the reverse Holder's inequality.Let[b,T]be the commutator generated by the Campanatotype function b∈■ and the Riesz transform associated with Schrdinger operator T=▽(-△+V)~(-1/2).In the paper,we establish the boundedness of[b,T]on Lebesgue spaces and Campanato-type spaces.     

Boundedness of High Order Commutators of Riesz Transforms Associated with Schrödinger Type Operators

Let L_2=(-?)~2+ V~2 be the Schr?dinger type operator, where V■0 is a nonnegative potential and belongs to the reverse H?lder class RH_(q1) for q_1 n/2, n ≥5. The higher Riesz transform associated with L_2 is denoted by ■and its dual is denoted by ■. In this paper, we consider the m-order commutators [b~m, R] and [b~m, R*], and establish the(L~p, L~q)-boundedness of these commutators when b belongs to the new Campanato space Λ_β~θ(ρ) and 1/q = 1/p-mβ/n.     

解析函数空间上的自伴加权复合算子

通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。     

Hölder Continuity of Spectral Measures for the Finitely Differentiable Quasi-Periodic Schrödinger Operators

In the present paper, we prove the $\frac{1}{2}$-Hölder continuity of spectral measures for the $C^{k}$ Schrödinger operators. This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrödinger cocycles in [5].     

WEIGHTED ESTIMATES FOR COMMUTATORS OF POTENTIAL OPERATORS ON SPACES OF HOMOGENEOUS TYPE

We derive some strong type and weak type weighted norm estimates which relate the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.     

A Note on the Convergence of the Schrödinger Operator along Curve

In this paper we set up a convergence property for the fractional Schödinger operator for $0相似文献