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If $T$ defined as $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded from $L^{\infty}$ to $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-normhttps://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

If $T$ defined as $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded from $L^{\infty}$ to $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

If $T$ defined as $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded from $L^{\infty}$ to $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. https://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

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If $T$ defined as $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded onfrom $L^{\infty}$ to $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

If $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded on $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

If $T$ defined as $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded from $L^{\infty}$ to $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm

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Danqing
Danqing
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Operators from $L^{\infty}$ to $L^{\infty}$

If $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded on $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from Page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.

I asked this question on StackExchange Mathematics before but nobody answered me. http://math.stackexchange.com/questions/428449/operators-from-l-infty-to-l-infty-below-bound-of-the-norm