We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal ...

The idea of difference sequences of real (or complex) numbers was introducedby Ki zmaz cite{Kizmaz}. In this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  Delta,mathcal{F}right)  .$ We study some of its properties likesolidity, symmetricity, etc.

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L1(G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

In this paper, we introduce the concepts of invariant convergence, lacunary invariant statistical convergence of sequences of fuzzy numbers and lacunary strongly invariant convergence of sequences of fuzzy numbers. We give some relations related to these concepts.

Let f be a 2π periodic function in L[0, 2π] and ∑∞ k=−∞ f̂(nk)e inkx be its Fourier series with ‘small’ gaps nk+1 − nk ≥ q ≥ 1. Here we have obtained sufficiency conditions for the absolute convergence of such series if f is of ∧ BV (p) locally. We have also obtained a beautiful interconnection between lacunary and non-lacunary Fourier series.

Using the Padé approximation of the exponential function, we obtain recurrence relations between Apostol-Bernoulli and between Apostol-Euler polynomials. As applications, we derive some new lacunary recurrence relations for Bernoulli and Euler polynomials with gap of length 4 and lacunary relations for Bernoulli and Euler numbers with gap of length 6.

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.