Sakin Demi̇r

activity

20202022

most citedVariational Inequalities For The Differences Of Averages Over Lacunary Sequences

4 citations · 4 across the 11 of their papers we have counts for

collaborators

11 papers

math.FA2022

Banach space valued $H^{p}$ spaces with $A_{p}$ weight

Sakin Demir

In this research we introduce the Banach space valued $H^{p}$ spaces with $A_{p}$ weight, and prove the following results: Let $A$ and $B$ Banach spaces, and $T$ be a…

math.CA2022

Variaiton and $λ$ -jump inequalities on $H^{p}$ spaces

Sakin Demir

Let $ϕ \in S$ with $\int ϕ (x) d x = 1$ , and define $ϕ_{t} (x) = \frac{1}{t ^{n}} ϕ (\frac{x}{t}),$ and denote the function family ${ϕ_{t} * f (x)}_{t > 0}$ by $Φ * f (x)$ . Suppose t…

math.CA2022★ 4 cited

Variational Inequalities For The Differences Of Averages Over Lacunary Sequences

Sakin Demir

Let $f$ be a locally integrable function defined on $R$ , and let $(n_{k})$ be a lacunary sequence. Define the operator $A_{n_{k}}$ by $$A_{n_k}f(x)=\frac{1}{n_k}\int_0^{n_k}f(…

math.CA2021

Variation and oscillation inequalities for operator averages on a complex Hilbert space

Sakin Demir

Let $H$ be a complex Hilbert space and $T : H \to H$ be a contraction. Let $A_{n} f = \frac{1}{n} j = 1 \sum n T^{j} f$ for $f \in H$ . Let $(n_{k})$ be a…

math.CA2021

Unconditional convergence of the differences of Fejér kernels on $L^{2} (R)$

Sakin Demir

Let $K_{n} (x)$ denote the Fejér kernel given by $K_{n} (x) = j = - n \sum n (1 - \frac{∣ j ∣}{n + 1}) e^{- ij x}$ and let $σ_{n} f (x) = (K_{n} * f) (x)$ , where as usual $f * g$ denotes the…

math.CA2020

Complete convergence of the Hilbert transform

Sakin Demir

Suppose that ${a_{j}} \in ℓ^{1}$ , and suppose that for any sequence $(t_{n})$ of integers there exits a constant $C_{1} > 0$ such that $$\sharp\left\{k\in\mathbb{Z}:\sup_{n\geq 1}\left|\…

math.CA2020

Oscillation inequalities on real and ergodic $H^{1}$ spaces

Sakin Demir

Let $(x_{n})$ be a sequence and $ρ \geq 1$ . For a fixed sequences $n_{1} < n_{2} < n_{3} < \dots$ , and $M$ define the oscillation operators $$\mathcal{O}_ρ(x_n)=\left(\sum_{k=1}^\infty\sup_{\subs…

math.CA2020

An extension of Calderon Transfer Principle

Sakin Demir

We first prove that the well known transfer principle of A. P. Calderón can be extended to the vector-valued setting and then we apply this extension to vector-valued inequalities…

math.CA2020

Weighted inequalities in ergodic theory via transference

Sakin Demir

We first extend Calderón's transfer principle to weighted spaces in various different settings under suitable assumptions. Then we apply our results for some inequalities on the re…

math.CA2020

A Sufficient Condition For An Operator To Map $u L^{\infty}$ to $BMO_{u}$

Sakin Demir

Let $T$ be an operator and suppose that there exists a positive constant $C$ such that $(\int_{I} ∣ T f (x) ∣^{q} d x)^{1/ q} \leq C (\int_{I} ∣ f (x) ∣^{q} d x)^{1/ q}$ for e…

math.CA2020

Inequalities For Variation Operator

Sakin Demir

Let $f$ be a measurable function defined on $R$ . For each $n \in Z$ define the operator $A_{n}$ by $A_{n} f (x) = \frac{1}{2 ^{n}} \int_{x}^{x + 2^{n}} f (y) d y .$ Consider the vari…

Banach space valued Hp spaces with Ap​ weight

Variaiton and λ-jump inequalities on Hp spaces

Variational Inequalities For The Differences Of Averages Over Lacunary Sequences

Variation and oscillation inequalities for operator averages on a complex Hilbert space

Unconditional convergence of the differences of Fejér kernels on L2(R)

Complete convergence of the Hilbert transform

Oscillation inequalities on real and ergodic H1 spaces

An extension of Calderon Transfer Principle

Weighted inequalities in ergodic theory via transference

A Sufficient Condition For An Operator To Map uL∞ to BMOu​

Inequalities For Variation Operator

Banach space valued $H^{p}$ spaces with $A_{p}$ weight

Variaiton and $λ$ -jump inequalities on $H^{p}$ spaces

Unconditional convergence of the differences of Fejér kernels on $L^{2} (R)$

Oscillation inequalities on real and ergodic $H^{1}$ spaces

A Sufficient Condition For An Operator To Map $u L^{\infty}$ to $BMO_{u}$