We study the boundedness and compactness of generalized Volterra integral operator on weighted Bergman spaces with doubling weights unit disc. A Toeplitz is defined boundedness, Schatten class membership this are investigated Hilbert space. As an application, operators also characterized. Finally, we get characterizations Hardy space $$H^2$$ .

Abstract In this paper, we obtain the best constant and equality condition for a class of mixed-norm Hardy inequalities when weight is power function. By building solving corresponding Euler equation, look optimal One main ingredients to introduce two key auxiliary functions so that equalities are derived.

We show that any pointwise multiplier for BMO(R) generates a function p from the class P(Rn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable L space. In particular, this gives a positive answer to Diening’s conjecture saying that there are discontinuous functions which nevertheless belong to P(Rn). Mathematics Subject Classification (2000): 42B25

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

We define the weighted Carleson measure space CMO w using wavelets, where the weight function w belongs to the Muckenhoupt class. Then we show that CMO w is the dual space of the weighted Hardy space H p w by using sequence spaces. As an application, we give a wavelet characterization of BMOw.

We give an example of an operator that satisfies the curvature condition as defined in [2], but is not similar to the backward shift S ∗ on the Hardy class H. We conclude therefore that the contraction assumption in the similarity characterization given in [2] is a necessary requirement.

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and Pólya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity condition. In this paper, we determine the best constant for a class of inequalities when the monotonicity condition is no longer satisfied. Mathematics subject ...

By selecting a certain subensemble of joint detection events in a two-particle interferometer arrangement, a formal nonlocality contradiction of the Hardy type is derived for an ensemble of particle pairs configured in the maximally entangled state. It is argued, however, that the class of experiments exhibiting this kind of contradiction does not rule out the assumption of local realism.

Using potential theoretic methods we give extension results for functions in various Hardy classes and in the Nevanlinna class in C". Our exceptional sets are polar or slightly larger n-small sets depending whether the majorant is a harmonic or separately hyperharmonic function.

MSC: primary 62H05 60E15 secondary 62M10 a b s t r a c t We generalize Hoeffding's lemma to apply to covariances between functions of several random variables. Our generalization leads to a new class of covariance inequalities involving the Vitali or Hardy–Krause variation. These inequalities are relevant to the study of weakly dependent processes. Published by Elsevier B.V.