In this article, we study the existence and multiplicity of nontrivial solutions for a class of Hamiltoniam systems with weights and nonlinearity involving the Hardy-Sobolev exponents. Results are proved using variational methods for strongly indefinite functionals.

We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L spaces if and only if the variable exponent p(x) ∼ const.

We show that the Hardy-Littlewood maximal operator and a class of CalderónZygmund singular integrals satisfy the strong type modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.

The principal objects of study in this thesis are the noncommutative Hardy algebras introduced by Muhly and Solel in 2004, also called simply “Hardy algebras,” and their quotients by ultraweakly closed ideals. The Hardy algebras form a class of nonselfadjoint dual operator algebras that generalize the classical Hardy algebra, the noncommutative analytic Toeplitz algebras introduced by Popescu i...

Let φ : ℝ(n) × [0, ∞)→[0, ∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, H(A)(φ)(ℝ(n)), via the grand maximal function. The authors then obtain some real-variable characterizations of H(A)(φ)(ℝ(n)) in terms of the radial, the nontangential, and the tangential maximal functions, which general...

Distinguished selfadjoint extension of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, −|x|. The method uses Hardy-Dirac inequalities and quadratic form techniques.

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space Morrey space. The theory developed generalize complement some already existing results.

A class of fractional derivative operators (with the Appell hypergeometric function in the kernel) is used here to define a new subclass of analytic functions and a coefficient bound inequality is established for this class of functions. Also, an inclusion theorem for a class of fractional integral operators involving the Hardy space of analytic functions is proved. The concluding remarks brief...