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pro vyhledávání: '"Demir, Sakin"'
Autor:
Demir, Sakin
In this research we introduce the Banach space valued $H^p$ spaces with $A_p$ weight, and prove the following results: Let $\mathbb{A}$ and $\mathbb{B}$ Banach spaces, and $T$ be a convolution operator mapping $\mathbb{A}$-valued functions into $\mat
Externí odkaz:
http://arxiv.org/abs/2209.04033
Autor:
Demir, Sakin
Let $\phi\in \mathscr{S}$ with $\int\phi (x)\, dx=1$, and define $$\phi_t(x)=\frac{1}{t^n}\phi (\frac{x}{t}),$$ and denote the function family $\{\phi_t\ast f(x)\}_{t>0}$ by $\Phi\ast f(x)$. Suppose that there exists a constant $C_1$ such that $$\sum
Externí odkaz:
http://arxiv.org/abs/2203.13905
Autor:
Demir, Sakin
Publikováno v:
New York Journal of Mathematics, Vol. 28, 2022, pp. 1099-1111
Let $f$ be a locally integrable function defined on $\mathbb{R}$, and let $(n_k)$ be a lacunary sequence. Define the operator $A_{n_k}$ by $$A_{n_k}f(x)=\frac{1}{n_k}\int_0^{n_k}f(x-t)\, dt.$$ We prove various types of new inequalities for the variat
Externí odkaz:
http://arxiv.org/abs/2203.02154
Autor:
Demir, Sakin
Let $\mathcal{H}$ be a complex Hilbert space and $T:\mathcal{H}\to \mathcal{H}$ be a contraction. Let $$A_nf=\frac{1}{n}\sum_{j=1}^nT^jf$$ for $f\in \mathcal{H}$. Let $(n_k)$ be a sequence satisfying $\beta \geq n_{k+1}/n_k\geq \alpha >1$ for all $k\
Externí odkaz:
http://arxiv.org/abs/2107.14030
Autor:
Demir, Sakin
Let $K_n(x)$ denote the Fej\'er kernel given by $$K_n(x)=\sum_{j=-n}^n\left(1-\frac{|j|}{n+1}\right)e^{-ijx}$$ and let $\sigma_nf(x)=(K_n\ast f)(x)$, where as usual $f\ast g$ denotes the convolution of $f$ and $g$. Let the sequence $\{n_k\}$ be lacun
Externí odkaz:
http://arxiv.org/abs/2101.03910
Autor:
Demir, Sakin
Suppose that $\{a_j\}\in \ell^1$, and suppose that for any sequence $(t_n)$ of integers there exits a constant $C_1>0$ such that $$\sharp\left\{k\in\mathbb{Z}:\sup_{n\geq 1}\left|\sum_{i\in \mathcal{B}_n-t_n} \!\!\!\raise{1.9ex}\hbox{$\scriptsize\pri
Externí odkaz:
http://arxiv.org/abs/2009.05822
Autor:
Demir, Sakin
Publikováno v:
Russian Mathematics, 2023, Vol. 67, No.3, pp. 42-52
Let $(x_n)$ be a sequence and $\rho\geq 1$. For a fixed sequences $n_1
Externí odkaz:
http://arxiv.org/abs/2006.13216
Autor:
Demir, Sakin
Publikováno v:
Asian Journal of Mathematical Sciences, Vol. 4, Issue 2, 2020, pp. 15-18
We first prove that the well known transfer principle of A. P. Calder\'on can be extended to the vector-valued setting and then we apply this extension to vector-valued inequalities for the Hardy-Littlewood maximal function to prove the vector-valued
Externí odkaz:
http://arxiv.org/abs/2004.00462
Autor:
Demir, Sakin
We show that Calder\'on's transfer principle can be extended to the weighted spaces and we also include some applications of our results.
Externí odkaz:
http://arxiv.org/abs/2002.07589
Autor:
Demir, Sakin
Publikováno v:
International J. Functional Analysis, Operator Theory and Applications, Vol. 14, 2022, pp. 13-17
Let $T$ be an operator and suppose that there exists a positive constant $C$ such that $$\left(\int_I|Tf(x)|^q\, dx\right)^{1/q}\leq C\left(\int_I|f(x)|^q\, dx\right)^{1/q}$$ for every $q$ which is near enough to $1$ and for every interval $I$ in $\m
Externí odkaz:
http://arxiv.org/abs/2002.01430