Under mild conditions on the weight function K we characterize lacunary series in the so-called QK spaces.

We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known new numbers.

The rational self-assembly of mono-lacunary Keggin clusters with 4d and 4f metal salts via a conventional method has yielded two novel polyoxometalate-based 4d-4f heterometallic compounds containing lacunary Keggin anions connected to ten metal atoms: {[Ag{Ag2(H2O)4}{Ln(H2O)6}2H ⊂ {SiW11Ln(H2O)4O39}2]·nH2O (Ln = Ce and n = 7 for 1, Ln = Pr and n = 3 for 2). Their structures were determined by s...

In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces Ḟ pq(R ) to L(R). Recently the second author, together with Xue and Yan, great...

In this paper, we shall discuss the weighted boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002 and the one given by authors. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces Ḟ pq (R) to L(R). Recently one of ...